Efficient filtering with a complex modulated filterbank

ABSTRACT

A filter apparatus for filtering a time domain input signal to obtain a time domain output signal, which is a representation of the time domain input signal filtered using a filter characteristic having an non-uniform amplitude/frequency characteristic, comprises a complex analysis filter bank for generating a plurality of complex subband signals from the time domain input signals, a plurality of intermediate filters, wherein at least one of the intermediate filters of the plurality of the intermediate filters has a non-uniform amplitude/frequency characteristic, wherein the plurality of intermediate filters have a shorter impulse response compared to an impulse response of a filter having the filter characteristic, and wherein the non-uniform amplitude/frequency characteristics of the plurality of intermediate filters together represent the non-uniform filter characteristic, and a complex synthesis filter bank for synthesizing the output of the intermediate filters to obtain the time domain output signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional Application of U.S. patent applicationSer. No. 11/469,790 filed Sep. 1, 2006, which claims priority to U.S.patent application Ser. No. 60/744,559 filed Apr. 10, 2006 (AttorneyDocket No. SCH00274PR) and to U.S. patent application Ser. No.60/762,592 filed Jan. 27, 2006 (Attorney Docket No. SCH00265PR) all ofwhich are incorporated herein in their entirety by this referencethereto.

TECHNICAL FIELD

The present invention relates to a filter apparatus and a method forfiltering a time domain input signal, a filter generator and a methodfor generating an intermediate filter definition signal, especially forthe field of encoding, decoding, manipulating and filtering of audiosignals, e.g. in the field of HRTF (head related transfer function).

BACKGROUND OF THE INVENTION

It has been shown in [P. Ekstrand, “Bandwidth extension of audio signalsby spectral band replication”, Proc. 1^(st) IEEE Benelux Workshop onModel based Processing and Coding of Audio (MPCA-2002), pp. 53-58,Leuven, Belgium, 2002], that a complex-exponential modulated filter bankis an excellent tool for spectral envelope adjustment of audio signals.One application of this feature is audio coding based on Spectral BandReplication (SBR). Other fruitful applications of a complex filter bankinclude frequency selective panning and spatialization for parametricstereo, see [E. Schuijers, J. Breebart, H. Purnhagen, J. EngdegArd: “Lowcomplexity parametric stereo coding”, Proc. 116^(th) AES convention,2004, paper 6073] and parametric multichannel coding, see [J. Herre etal.: “The reference model architecture for MPEG spatial audio coding”,Proc. 118^(th) AES convention, 2005, paper 6447]. In those applicationsthe frequency resolution of the complex filter bank is further enhancedat low frequencies by means of sub-subband filtering. The combinedhybrid filter bank hereby achieves a frequency resolution that enablesthe processing of spatial cues at a spectral resolution which closelyfollows the spectral resolution of the binaural auditory system.

In some applications, however, the resolution of the filter bank isstill insufficient, in the sense that simple gain modifications in eachsubband do not suffice to truthfully model the action of a given filter.For binaural rendering of multi-channel audio by means of HRTF (headrelated transfer function) related filtering, the intricate phasecharacteristics of the filters are important for the perceived audioquality. It is of course possible to apply fast convolution methodsbased on the DFT (Discrete Fourier Transform) as a post-process to themulti-channel rendering, but if the rendering device already containsthe signals in the subband domain of complex exponential modulatedfilter bank, there are significant advantages in terms of computationalcomplexity and algorithmic integration in performing the HRTF derivedfiltering in the subband domain, which will be outlined in more detaillater. Since HRTF's are different for each individual and the derivedfilters depend on virtual source and/or listener positions which can forinstance be changed by control signals, user interfaces or by otherdescription signals, it is also important to be able to efficientlyconvert a given HRTF related filter into subband domain filters.

It is therefore the object of the present invention to provide a filterapparatus for filtering a time domain input signal, a method forfiltering a time domain input signal, a filter generator or a method forproviding an intermediate filter definition signal, which allow a moreefficient or a more flexible manipulation of a time domain input signalwith a better quality.

This object is achieved by a filter apparatus according to claim 1, by amethod for filtering a time domain input signal according to claim 41, afilter generator according to claim 25, a method for providing anintermediate filter definition according to claim 42, a system accordingto claim 40, a computer program according to claim 43 or a computerprogram according to claim 44.

SUMMARY OF THE INVENTION

An embodiment of the present invention relates to a filter apparatus forfiltering a time domain input signal to obtain a time domain outputsignal, which is a representation of the time domain input signalfiltered using a filter characteristic having a non-uniformamplitude/frequency characteristic comprising a complex analysis filterbank for generating a plurality of complex subband signals from the timedomain input signal, a plurality of intermediate filters, wherein oneintermediate filter is provided for each complex subband signal, whereinat least one of the intermediate filters of the plurality ofintermediate filters has a non-uniform amplitude/frequencycharacteristic, wherein the plurality of intermediate filters have ashorter impulse response compared to an impulse response of a filterhaving the filter characteristic, and wherein the non-uniformamplitude/frequency characteristic of the plurality of intermediatefilters together represent the non-uniform filter characteristic, and acomplex synthesis filter bank for synthesizing the output of theintermediate filters to obtain the time domain output signal.

As a second aspect, a further embodiment of the present invention is afilter generator for providing an intermediate filter definition signalcomprising a complex modulated filter bank for filtering an impulseresponse signal indicative of an amplitude/frequency filtercharacteristic in a time domain to obtain a plurality of complex valuedsubband signals as the intermediate filter definition signal, whereineach complex valued subband signal of the complex modulated filter bankcorresponds to an impulse response for an intermediate filter for asubband signal, wherein at least one of the complex valued subbandsignals comprises at least two different non-vanishing values, andwherein each complex valued subband signal is shorter than the impulseresponse signal.

Embodiments of the first aspect of the present invention are based onthe finding that a more efficient and/or a more flexible filtering (ormanipulation) of a time domain input signal can be achieved in thesubband domain, which is sometimes also referred to as QMF domain(quadrature mirror filter), with a better quality compared to othermanipulation schemes. The gain with respect to efficiency, especiallycomputational efficiency, is a consequence of the shorter impulseresponses of the intermediate filters compared to the impulse responseof a filter having the non-uniform filter characteristic in the timedomain and the fact that the subband signals can be processedindependently from one another. Due to the shorter impulse responses anembodiment of a filter apparatus can process each complex subbandsignals output by the complex analysis filter bank individually. Hence,the filtering can be carried out parallely, which speeds up theprocessing of the time domain input signal dramatically compared tomanipulating the time domain input signal directly due to the shorterimpulse responses.

Embodiments according the first aspect of the present invention areespecially favorable when it comes to balancing computational efficiencyon the one hand and quality on the other hand. While a direct processingof the time domain input signal in the time domain can be achieved by aconvolution with the impulse response of a filter having the non-uniformamplitude/frequency characteristic, which usually leads to a very goodquality, the convolution requires a high computational effort because ofthe length of the impulse response of the filter in the time domain.

On the other hand, transforming an audio signal into the frequencydomain by performing a Fourier transformation represents the tremendousdrawback that other manipulations, which are necessary in modernacoustical systems, cannot be efficiently performed in the Fourierdomain with a high quality.

Hence, by employing a plurality of intermediate filters, each having ashorter impulse response compared to an impulse response of a filterhaving the filter characteristic of a corresponding filter in the timedomain, of which at least one has an impulse response with at least twonon-vanishing values represents a highly favorable compromise betweencomputational efficiency on the one hand and quality on the other hand.As a consequence, embodiments of inventive filter apparatuses representan excellent compromise between a direct processing of the time domaininput signal for instance by means of convoluting the time domain inputsignal with the longer impulse response indicative of the non-uniformfilter characteristic, which leads to an enormous computational effort,and employing a Fourier transform, which leads to more problems in thefurther course of processing the signals.

The advantages of the embodiments of the first aspect of the presentinvention unfold especially in the context of FIR-filters (final impulseresponse), as each of the intermediate filters of the plurality ofintermediate filters has a significantly shorter impulse responsecompared to the impulse response of the FIR-filter in the time domain.Hence, by parallely processing the different subband signals output bythe complex analysis filter bank the computational efficiency candrastically be improved. This aspect is especially important in thefield of filters having long impulse responses. One field ofapplication, in which filters with very long impulse responsesfrequently occur, are HRTF-related applications (HRTF=head relatedtransfer function), like for instance down-mixing multiple channel audiosignals for feeding to headphones, other head-related speaker systems orstereo sound systems.

In many concrete applications the computational efficiency is even moreincreased, as the audio signals are already present in the (complex)subband or QMF domain. Hence, in many concrete implementations, thecomplex analysis filter bank and the complex synthesis filter bank forgenerating the plurality of complex subband signals from the time domaininput signal and for synthesizing the time domain output signal arealready present.

With respect to the second aspect, embodiments of the present inventionare based on the finding that a more flexible and more efficientfiltering of the time domain input signal with a better quality can beachieved by providing an intermediate filter definition signal, whichcan for instance be provided to a filter apparatus according to thefirst aspect to define its intermediate filters.

A significant advantage of embodiments according to the second aspect ofthe present invention is that an intermediate filter definition signalfor a set of intermediate filters is obtained by providing an embodimentof the inventive filter generator with a filter defining signal, such asan impulse response signal indicative of an amplitude/frequency filtercharacteristic of a filter in the time domain or other filter definitionsignals. Hence, an embodiment of a filter generator provides a filterdefinition signal for a set of intermediate filters to effectively thesame filtering as a filter in the time domain defined by the filterdefinition signal virtually without introducing aliasing effects. As aconsequence, embodiments of an inventive filter generator enable avirtually alias free performance, of an arbitrary filter in the subbanddomain. By utilizing an embodiment of the inventive filter generatorarbitrary filter characteristics can be transferred from the time domainto the subband signal domain, like virtually alias free equalization,low-pass filter characteristics, high-pass filter characteristics,band-pass filter characteristics, band-rejection filter characteristics,resonance filter characteristics, notch filter characteristics or morecomplex filter characteristics. Among the more complex filtercharacteristics, a combination of several characteristics as well asHRTF-related filter characteristics are important to mention.

Especially in the context of HRTF-related applications in the field ofmulti-channel audio systems and other high quality applications it isimportant to note that embodiments of the inventive filter generatorenable to truthfully model an action of a given filter in the timedomain in the subband domain. The virtually alias free performance,which is especially important in HRTF-related applications, is madepossible as the phase characteristics of a filter in the time domain is(almost) perfectly transferred into the subband domain. Examplesillustrating this will be outlined in the further course of the presentapplication.

Among the advantages of embodiments of the second aspect of the presentinvention is especially the significant gain with respect to theachievable computational efficiency. The complex modulated filter banksof embodiments of the inventive filter generator produce a plurality ofcomplex valued subband signals as the intermediate filter definitionsignal, wherein each of the complex valued subband signal is shorterthan the impulse response signal indicative of the amplitude/frequencyfilter characteristic in the time domain. The filter generator, hence,produces an intermediate filter definition signal comprising the outputof the complex modulated filter bank with its plurality of short complexvalued subband signals, which does not only enable a fast, efficient andparallel computation with respect to filtering a time domain inputsignal to obtain a time domain output signal in the frame work of anembodiment of a filter apparatus, but does also enable a fast, efficientand parallel computation of the intermediate filter definition signalitself. Compared to a direct application of the impulse response signalindicative of the amplitude/frequency filter characteristic in the timedomain by convoluting the impulse response signal with the time domaininput signal, the application of an embodiment of an inventive filtergenerator according to the second aspect of the present inventionenables a simplified, faster and more efficient computation, which leadsto an audibly indistinguishable result compared to the more complexconvolution method.

Furthermore, an embodiment of the inventive filter generator also offersthe advantage of a significantly enhanced flexibility with respect tothe possible filter characteristics applied in the subband domain. Asarbitrary filter characteristics can be transferred from the time domainto the subband domain by an embodiment of an inventive filter generator,an enormous flexibility is introduced to audio signal processing andmanipulation. For instance, an embodiment of an inventive filtergenerator is capable of providing an intermediate filter definitionsignal corresponding to an individually altered filter characteristic ofan HRTF-related filter. In the field of HRTF this offers the opportunityto individually modify the HRTF filters according to the needs andhearing capabilities of an individual. Moreover, the source position aswell as the listener position with respect to each other and withrespect to a (simulated or calculated) environment (e.g. a concert hall,an open space, a stadium) can be adapted. This offers the greatadvantage of providing a listener with a great flexibility with respectto the acoustic conditions. An embodiment of the inventive filtergenerator, hence, provides the possibility to virtually switch from astadium to a concert hall or an open field, without employing thenecessity to transfer the audio signals between the time domain, thesubband domain and/or the frequency domain. By employing an embodimentof an inventive filter generator all these manipulations of the audiosignal can be performed inside the subband domain with a very highquality, which is perceptually indistinguishable from a signalprocessing in the time domain, but which offers an enormouscomputational efficiency improvement.

This flexibility is not only limited to switching from one environmentto another, e.g. switching from a stadium to a concert hall and visaversa. An embodiment of an inventive filter generator offers thepossibility to alter the filter characteristics of the plurality of theintermediate filters in a quasi-continuous fashion. An application inthe field of HRTF is an application of an embodiment of the filtergenerator and/or of the filter apparatus in a head tracking application,in which for instance the position of the listener with respect todifferent audio sources varies in a quasi-continuous way. Possibleapplications comprise, for instance, simulations and computer games witha very high quality.

Another advantage of an embodiment of a filter generator is that theapplication of an embodiment of a filter generator is more efficientwith respect to the memory usage, as an impulse response signal providedto the complex modulated filter bank of the filter generator istypically a real valued signal, whereas the intermediate filterdefinition signal is a complex valued signal of approximately the sameover-all length. As a consequence, storing the impulse response signalscompared to the intermediate filter definition signals (or the filtertaps of the intermediate filters) saves memory, roughly speaking, of anorder of 2. Due to the possibility of a fast and efficient parallelcomputation, especially in the field of memory-sensitive applicationscomprising a great parameter space with respect to the possible impulseresponse signals, this represents a significant advantage.

In one embodiment of in an inventive filter generator the filtergenerator is provided with a filter definition signal, which cancomprise for instance the filter taps of a digital filter in the timedomain or by a transfer function in the frequency domain, which cancomprise the amplitude/frequency characteristic and/or thephase/frequency characteristic of a filter. In these cases, anembodiment of the filter generator furthermore comprises an impulseresponse signal generator, which provides the appropriate impulseresponse signal indicative of the resulting amplitude/frequency filtercharacteristic in the time domain to the complex modulated filter bankof the filter generator. Hence, the inclusion of an impulse responsesignal generator in some embodiments of an inventive filter generatoroffers an even more flexibility with respect to providing theintermediate filter definition signal, as not only the impulse responsesignals in the form of discrete time signals can be provided to anembodiment of the filter generator but also the filter taps or thefrequency domain description of a filter in the time domain can betransferred into the subband domain by an appropriate embodiment of afilter generator.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described by way of illustrativeexamples, not limiting the scope or spirit of the invention, withreference to the accompanying drawings, in which:

FIG. 1 a illustrates the processing of a digital audio signal by meansof subband filtering in a system comprising a filter generator and afilter apparatus;

FIG. 1 b illustrates a possible solution for a complex analysis bank;

FIG. 1 c illustrates a possible solution for a complex synthesis filterbank;

FIG. 1 d illustrates a further possible solution for a complex synthesisfilter bank;

FIG. 1 e illustrates an interplay of an embodiment of a filter generatorwith a plurality of intermediate filters of an embodiment of a filterapparatus;

FIG. 2 illustrates the processing of a digital audio signal by means ofdirect form filtering;

FIG. 3 illustrates a preferred embodiment of a system with a filterconverter;

FIG. 4 illustrates a given filter impulse response;

FIG. 5 illustrates an impulse response obtained by complex gainadjustment of subbands;

FIG. 6 illustrates the magnitude response of a given filter;

FIG. 7 illustrates the magnitude response of a filter obtained bycomplex gain adjustment of subbands;

FIG. 8 compares the performance of the present invention with complexgain adjustment of subbands;

FIG. 9 illustrates a preferred embodiment of a filter apparatuscomprising an optional embodiment of a filter generator and furthercomponents;

FIG. 10 illustrates a filter characteristic along with several frequencybands for different subbands; and

FIG. 11 illustrates a preferred embodiment of a filter generator.

DESCRIPTION OF PREFERRED EMBODIMENTS

The below-described embodiments are merely illustrative for theprinciples of the present invention of efficient filtering with acomplex modulated filterbank. It is understood that modifications andvariations of the arrangements and the details described herein will beapparent to others skilled in the art. It is the intent, therefore, tobe limited only by the scope of the impending patent claims and not bythe specific details presented by way of description and explanation ofthe embodiments herein.

In the following, objects with the same or similar functional propertiesare denoted with the same reference signs. Unless explicitly notedotherwise, the description with respect to objects with similar or equalfunctional properties can be exchanged with respect to each other.

FIG. 1 a illustrates in the form of a system comprising embodiments ofboth a filter apparatus and a filter generator the processing of adigital audio signal by means of subband filtering according to thepresent invention. This signal path can for instance represent a part ofa spatial audio rendering system where the input is a received audiochannel and the output is a component of a signal to be played back atthe right ear. The input signal (Digital audio signal or time domaininput signal) is analyzed by the complex analysis bank 101 by means offiltering with a set of L analysis filters followed by downsampling of afactor L, wherein L is a positive integer, preferably larger than 1.Typically the factor L is a power of 2, preferably L=64. The analysisfilters are usually obtained by a complex modulation of a prototypefilter p(v), wherein ν is a positive integer indicating an index in anarray of data or an index of a value in a signal not downsampled byfactor L. The output of the filter bank consists of L subband signalsthat are processed by a subband filtering 102. This subband filteringconsists of a combination of manipulations such as subband gainadjustment according to received control data and application of finiteimpulse response filters applied separately in each subband. The filtertaps of the subband filters are obtained from an (inventive) filterconverter 104 as an embodiment of a filter generator which takes asinput a filter described by direct form filter taps, a frequency domaindescription or an impulse response (signal). The complex synthesis bank103 reconstructs an output signal by means of upsampling by a factor L,filtering by L synthesis filters, summation of all the results, andextraction of the real part. The summation of all the results and theextraction of the real part can also be switched with respect to theirorder, as will be outlined more closely with respect to FIGS. 1 c and 1d.

FIG. 1 b shows a complex analysis bank 101 in more detail. The complexanalysis bank 101 comprises a plurality of L intermediate analysisfilters 120 for each subband to be output by complex analysis bank 101.To be more precise, each of the L intermediate analysis filters 120 isconnected in parallel to a node 130 to which the time domain inputsignal to be processed is provided. Each of the intermediate analysisfilters 120 is adapted for filtering the input signal of the complexanalysis bank 101 with respect to a center frequency of each subband.According to the center frequencies of the different subbands, eachsubband is labeled by a subband index or index n, wherein n is anon-negative integer, typically in the range from 0 to L−1. Theintermediate analysis filters 120 of the complex analysis bank 101 canbe derived from a prototype filter p(ν) by a complex modulationaccording to the subband index n of the subband to which theintermediate analysis filter 120 is applied. More details concerning thecomplex modulation of a prototype filter are explained below.

Either directly by the intermediate analysis filters 120 or by anoptional downsampler 140 (denoted by doted line in FIG. 1 b) thesampling frequency of the signal output by the intermediate analysisfilter bank 120 is reduced by a factor L. As mentioned before, thedownsamplers 140 supplied to each subband signal output by thecorresponding intermediate analysis filters 120 are optional as,depending on the concrete implementation, the downsampling can also becarried out in the frame work of the intermediate analysis filters 120.In principle, downsampling the signal output by the intermediateanalysis filters 120 is not required. Nevertheless, the presence of theexplicit or implicit downsamplers 140 is a preferred option as theamount of data provided by the complex analysis bank 101 wouldalternatively be raised by a factor of L, leading to a significantredundancy of data.

FIG. 1 c illustrates a possible solution for a complex synthesis bank103. The complex synthesis bank 103 comprises L intermediate synthesisfilters to which the L subband signals from the subband filtering 102are provided to. Depending on the concrete implementation of the complexsynthesis bank 103 prior to the filtering in the frame work of theintermediate synthesis filters 150, the subband signals are upsampled byL upsampler 160, which reconstruct the sampled frequency of the subbandsignals by increasing the sampling frequency by a factor of L. In otherwords, the optional upsampler 160 reconstruct or reform the subbandsignals provided to the upsampler 160 in such a way that the informationcontained in each of the subband signals is retained while the samplingfrequency is increased by a factor of L. Nevertheless, as alreadyexplained in the context of FIG. 1 b, the upsamplers 160 are optionalcomponents, as the upsampling can also be carried out in the frame workof the intermediate synthesis filters 150. Hence, the step of upsamplingthe subband signals carried out by the upsampler 160 can besimultaneously processed in the frame work of the intermediate synthesisfilers 150. If, however, the downsamplers 190 are neither explicitly norimplicitly implemented, the upsamplers 160 do not have to be implementedexplicitly or implicitly.

The intermediate synthesis filters 150 are connected via an output to anadder 170 which sums up the filtered subband signals output by the Lintermediate synthesis filters 150. The adder 170 is further connectedto a real part extractor 180, which extracts or forms a real valuedsignal or rather a (real valued) time domain output signal based on thecomplex valued signal provided by the adder 170. The real part extractor180 can perform this task for instance by extracting the real part of acomplex valued signal provided by the adder 170, by calculating theabsolute value of the complex valued signal provided by the adder 170 orby another method that forms a real valued output signal based on acomplex valued input signal. In the case of the system shown in FIG. 1a, the signal output by the real part extractor 180 is the time domainoutput signal output by the embodiment of the inventive filterapparatus.

The second possible solution for a complex synthesis bank 103 shown inFIG. 1 d differs from the first possible solution shown in FIG. 1 c onlyconcerning the real part extractors 180 and the adder 170. To be moreprecise, the outputs of the intermediate synthesis filters 150 areconnected separately from each subband to a real part extractor 180extracting or forming a real valued signal based on the complex valuedsignal output by the intermediate synthesis filters 150. The real partextractor 180 are then connected to the adder 170, which sums up the Lreal valued signals derived from the L filtered subband signals to formthe real valued output signal provided by the adder 170, which in thecase of the system shown in FIG. 1 a is the time domain output signal.

FIG. 1 e shows the subband filtering 102 and its interplay with thefilter converter 104 in more details. The subband filtering 102comprises a plurality of intermediate filters 190, wherein oneintermediate filter 190 is provided for each complex valued subbandsignal provided to the subband filtering 102. Hence, the subbandfiltering 102 comprises L intermediate filters 190.

The filter converter 104 is connected to each of the intermediatefilters 190. As a consequence, the filter converter 104 is capable ofproviding the filter taps for each of the intermediate filters 190 ofthe subband filtering 102. More details concerning the filtering done bythe intermediate filters 190 will be explained in the further course ofthe application. Hence, the filters taps provided to the differentintermediate filters 190 and output by the filter converter 104 form theintermediate filter definition signal.

Furthermore, it should be noted that the embodiments, solutions andimplementations can comprise additional and/or optional delays fordelaying any of the signals or a subset of signals, which have beenomitted in FIG. 1 a to 1 e for the sake of simplicity. Also in the FIGS.2 to 11 optional delays have been omitted for the sake of simplicity.Nevertheless, delays or delayers can be comprised in elements shown(e.g. filters) or added as optional elements in all embodimentsdepending on their concrete implementation.

FIG. 2 illustrates the processing of a digital audio signal by means ofdirect form filtering 201. If the same filter is given as input to thefilter converter 104 of FIG. 1 and the direct filtering 201, a designgoal for the filter converter 104 is that the digital audio output of103 should be perceptually (or audibly) indistinguishable from thedigital audio output of the direct filtering 201, if the digital audioinputs to the complex analysis bank 101 and the direct filtering 201 areidentical and the processing in the direct filtering 102 consists ofpure stationary subband filtering.

In the embodiment of the system shown in FIG. 1 a to FIG. 1 e the filterinput to the filter converter 104 is given as a filter definitionsignal, which can for instance comprise the filter taps of acorresponding time domain filter, a frequency domain description(amplitude/frequency characteristic and/or phase/frequencycharacteristic) or an impulse response signal of the appropriate filter.

In the case of the direct filtering 201 the same filter definitionsignal can in principle be used. Depending on the concreteimplementation and the filter definition signal, the filtering can becarried out by direct application of the filter taps in the frame work adigital filter, by a discrete Fourier transform along with a transferfunction or another frequency domain description or by means ofconvolution with the impulse response signal.

FIG. 3 illustrates a preferred embodiment of a filter converter 104according to the present invention as an embodiment of a filtergenerator. The filter is assumed to be given by its impulse response.Viewing this impulse response as a discrete time signal, it is analyzedby an L-band complex analysis (filter) bank 301. The resulting subbandsignal outputs are then exactly the impulse responses of filters to beapplied separately in each subband in the subband filtering 102. In thepreferred embodiment shown in FIG. 3, the filter definition signalprovided to the filter converter 104 and its complex analysis bank orcomplex analysis filter bank 301 is the impulse response signalindicative of the amplitude/frequency characteristic of a filter, whichis to be transferred into the subband domain. Hence, the output of thecomplex analysis (filter) bank 301 of each of the L subbands representsthe impulse response of the intermediate filters comprised in thesubband filtering 102.

The complex analysis bank 301 is in principle derived from the analysisbank 101 but it has a different prototype filter and a slightlydifferent modulation structure, the details of which will be outlined inthe following description. The same fast algorithms that are used for animplementation of the complex analysis bank 101 can be reused forcomplex analysis bank 301, leading to a very fast and very efficientconversion process.

Moreover, the length of the prototype filter q(v) can be designed to beonly a fraction of the length of the prototype filter p(v). Due to thedownsampling by a factor L, the length of subband filters are also afactor of L smaller than the sum of the lengths of the given time domainfilter and the prototype filter q(v). The computational effort is thusreduced in comparison to the direct form filtering 201 by approximatelya factor of L/4. The offset factor of 4 is due to the replacement ofreal filtering with complex filtering. Another offset is thecomputational cost of the complex analysis and synthesis banks 101 and103. For efficient implementations this cost is comparable to the costof rather short FIR filters, and hence negligible, as outlined before.Moreover, this offset of the reduction in computational cost does notexist for systems that already employs these two filter banks 101 and103.

FIG. 4 illustrates an example of a given filter impulse response 400. Itconsists of 192 (=64·3) nonzero taps. In other words, the impulseresponse 400 shown in FIG. 4 comprises 192 non-vanishing values.

In the present application, a non-vanishing tap or value is a tap or avalue which is ideally not equal to zero. Nevertheless, due toimplementation restraints in the frame work of this application anon-vanishing value or tap is a real valued or complex valued tap orvalue with an absolute value which is larger than a predeterminedthreshold, e.g. 10^(−s) or 2^(−s), wherein s is a positive integerdepending on the requirements of a concrete implementation. In digitalsystems this threshold is preferably defined in the binary system (basis2), wherein the integer s has a predetermined value depending on thespecifics of the implementation. Typically, the value s is 4, 5, 6, 7,8, 10, 12, 14, 16 or 32.

The impulse response 400 of the system of FIG. 1 is indistinguishablefrom this given impulse response at the resolution of the image, in acase where a L=64 band filterbank with a prototype filter of length 640(=64·10) is applied and a prototype filter of length 192 (=64·3) is usedfor the filter converter 104 of FIG. 3. The corresponding intermediatesubband filters have only 5 (=3+3−1) taps each, as will be explainedlater.

FIG. 5 illustrates the impulse response 410 of the system of FIG. 1 witha 64 band filterbank, in a special case corresponding to prior art usagefor envelope adjustment and equalization. In this case, the subbandfilters or rather intermediate filters 190 are all of one tap only, so aconstant complex gain is applied to each subband. For each subband, thecorresponding gain is chosen to be equal to the complex frequencyresponse of the filter of FIG. 4 evaluated at the center frequency ofthe particular subband. As it can be seen from the result, there aresevere pre-echo artifact and there will be a significant perceptualdifference between the application of this filter response compared tothe target impulse response 400 of FIG. 4.

FIG. 6 illustrates the magnitude response 420 of the filter of FIG. 4.The frequency scale of FIG. 6 is adjusted to the resolution of a 64 bandfilter bank (L 64).

FIG. 7 illustrates the magnitude response 430 of the filter underlyingthe impulse response 410 shown in FIG. 5. As it can be seen, the usageof only one gain per subband results in a poor approximation to thedesired frequency response. The main reason for this is the fastvariation of the target phase spectrum. In fact, this prior art methodis better suited at modeling linear phase responses.

FIG. 8 finally compares the performance of an embodiment of the presentinvention and of the prior art method of complex gain adjustment ofsubbands. The dotted curve is a redrawing of the target magnituderesponse 420 of FIG. 6. The dashed curve 440 is the magnitude responseof the difference between the complex frequency responses of the targetfilter and its approximation by the prior art method. The solid curve450 is the magnitude response of the difference between the complexfrequency responses of the target filter and its approximation by themethod taught by the present invention with the parameters as discussedduring the description of FIG. 4. As it can be seen, the error of theprior art method is small only at the 64 midpoints of filter banksubbands whereas the inventive method leads to an approximation qualityin the 50 dB range. It should be pointed out that this is also the levelof performance one measures when comparing the output of the inventivesystem to the output of the reference system for an arbitrary inputsignal.

As the comparison of the two curves 440 and 450 in FIG. 8 shows, anembodiment of an inventive filter apparatus, an embodiment of a filtergenerator and a system comprising both embodiments offer a significantadvantage concerning the quality of the manipulation of an input signal.The significant difference concerning the quality of filtering (ormanipulation) of the input signal outlined above is a consequence of thefact that at least one of the intermediate filters 190 has an impulseresponse with two or more non-vanishing values. In other words, at leastone of the intermediate filters 190 comprises at least two non-vanishingfilter taps. Furthermore, it is important to note that the number ofsubbands L processed by an embodiment of a filter apparatus is larger orat least equal to 2. Nevertheless, the number of subbands L issignificantly smaller than the number of frequency bands required for acomparable quality in the case of a Fourier transform-based filteringcombined with a filter mainly described by an amplitude/frequencycharacteristic and/or a phase/frequency characteristic as the transferfunction of the filter.

Due to the fact that the impulse response of the intermediate filters190 are significantly shorter than the impulse response of theunderlying filter characteristic in the time domain, the computationswith respect to each subband can be carried out significantly faster.Furthermore, as the different subband signals can be processedindependently, both an embodiment of the filter apparatus as well as anembodiment of the filter generator 104 can process the respective inputsignals highly efficiently in a fast and a parallel manner. Hence, theprocessing of both a digital audio input as an input signal as well asan impulse response indicative of a filter characteristic can be carriedout highly efficiently in a parallel fashion. As outlined earlier, anembodiment of an inventive filter apparatus as well as an embodiment ofan inventive filter generator combine the advantages of both a directprocessing of audio signals in the time domain leading to a very highquality and using a combination of a Fourier transform along with atransfer function in the frequency domain offering a high efficiency aseach frequency band is only multiplied with a (complex or real valued)tap in the process of filtering the signal.

On the other hand, the disadvantages of both, purely processing theinput signals in the time domain, which leads to an enormous computationeffort, and those of a Fourier transform, can be significantly reducedand suppressed to a level that the output of an embodiment of a filterapparatus is perceptually indistinguishable from the quality of a directprocessing in the time domain.

These two advantages offer a great flexibility for filtering digitalsignals with varying filtering characteristics. This is especiallyimportant in the field of HRTF, as HRTF-related filters usually have avery long impulse response. Hence, an embodiment of an inventive filterapparatus comprising a complex analysis filter bank 101, a plurality ofintermediate filters 190 in the subband filtering 102 and a complexsynthesis filter bank 103 offers especially in the field of HRTF-relatedapplications significant computational advantages due to the possibleparallel processing of subband signals.

Embodiments of a filter generator and embodiments of systems comprisingboth a filter apparatus and a filter generator offer furthermore theadvantage that filters can easily be adapted to specific environments,parameters or other specific needs of the application at hand.Especially in terms of HRTF-related applications, an embodiment of sucha system can be used in head-tracking applications, in which severalsources of sounds and noises as well as the position of the listenervary over time. Such an embodiment of a system comprising a filterapparatus and a filter generator therefore offer a highly efficient andflexible way to present an audio impression of a three dimensionalarrangement of sound sources with respect to a varying position andorientation of a hypothetical listener via headphones or otherhead-related sound systems (stereo sound systems).

As this last example illustrates, an embodiment of an inventive filterapparatus along with an inventive filter generator offers not only ahighly efficient system for audio manipulation with an excellent qualitybut also a very flexible way to introduce altering audio impressions inan efficient way.

Complex Modulated Filter Banks

In the following, let

${Z(\omega)} = {\sum\limits_{v = {- \infty}}^{\infty}{{z(v)}{\exp \left( {{- \; }\; v\; \omega} \right)}}}$

be the discrete time Fourier transform of a discrete time signal z(v).As before, ν is an integer indicating an index or a time index of a timesignal, while ω=2π·f is the circular frequency associated to thefrequency f, π is the circular number (π=3.1415926 . . . ) andi=j=√{square root over (−1)} is the imaginary unit.

The complex exponential modulated L-band filterbank is defined from areal valued prototype filter p(v) of finite length. For the computationsbelow it will be assumed by extension with zeros that the prototypefilter is defined for all integers v. Given a real valued discrete timesignal x(v) the analysis filter bank 101 applies, as already explained,the complex modulated prototype filters followed by downsampling by afactor L in order to output the subband signals,

$\begin{matrix}{{{c_{n}(k)} = {\sum\limits_{v = {- \infty}}^{\infty}{{x\left( {v + {kL}} \right)}{p(v)}{\exp \left( {{- }\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)\left( {v + \theta} \right)} \right)}}}},} & (1)\end{matrix}$

for each subband index n=0, 1, . . . , L−1, and integer time index k.The time index k differs from the time index ν with respect to the factthat k refers to the downsampled signals, whereas the integer ν withersto signals with the full sample frequency.

Given complex valued subband signals d_(n)(k), the synthesis filter bank103 applies filtering followed by upsampling by a factor of L and a realvalue extraction in order to output the real valued signals, as alreadyexplained, to obtain the output signal

$\begin{matrix}{{y(v)} = {{Re}{\left\{ {2\; L{\sum\limits_{k = {- \infty}}^{\infty}{\sum\limits_{n = 0}^{L - 1}{{d_{n}(k)}{p\left( {v - {kL}} \right)}{\exp \left( {\frac{\pi}{L}\begin{matrix}\left( {n + \frac{1}{2}} \right) \\\left( {v - {kL} + \psi} \right)\end{matrix}} \right)}}}}} \right\}.}}} & (2)\end{matrix}$

In the equations (1) and (2) θ and ψ represent (constant) phase factorsfor filtering the real valued discrete time signal x(ν) into complexvalued subband signal and for reconstructing real valued output samplesy(ν) from complex valued subband signals d_(n)(k). It is well known thata prototype filter and fixed phase factors θ and ψ can be chosen to giveperfect reconstruction, y(v)=x(v), in the case where d_(n)(k)=c_(n)(k),that is when the subband signals are unaltered. In practice, the perfectreconstruction property will hold true up to a delay (and/or a signchange), but in the computations that follow, this detail will beignored by allowing the use of an acausal prototype filter. The presentinvention is applicable to the pseudo QMF type of design as taught byPCT/SE02/00626 “Aliasing reduction using complex exponential modulatedfilter banks”. Here the prototype filter is symmetric p(−v)=p(v), andits discrete time Fourier transform P(ω) essentially vanishes outsidethe interval |ω|≦π/L. The perfect reconstruction is also replaced by anear-perfect reconstruction property. For the derivation that follows itwill be assumed for simplicity that both perfect reconstruction holdsand that P(ω)=0 for π/L<|ω|≦π. Moreover, the phase factors are assumedto satisfy the condition that ψ−θ is equal to an integer multiple of 4L.

In a critically sampled filter bank, the alteration of subband signalsprior to synthesis usually leads to the introduction of aliasingartifacts. This is overcome here due to the fact that an oversampling bya factor two is introduced by using complex valued signals. Although thetotal sampling rate of the subband samples is identical to the samplingrate of the discrete time input signal, the input signal is real valuedand the subband samples are complex valued. As it will be outlinedbelow, the absence of alias opens the door for efficient time invariantsignal processing.

Subband Filtering in a Complex Modulated Filter Bank

Consider the modification of subband filtering 102 of each subbandsignal obtained by filtering the analysis samples c_(n)(k) from thecomplex analysis bank 101 with a filter with impulse response g_(n)(k)prior to the synthesis (2) performed by the complex synthesis (filter)bank 103

$\begin{matrix}{{d_{n}(k)} = {\sum\limits_{l}{{g_{n}(l)}{{c_{n}\left( {k - l} \right)}.}}}} & (3)\end{matrix}$

Elementary computations show that given the assumptions on the frequencyresponse of the prototype filter, the resulting effect on thereconstructed time signal is that of a discrete time filtering

Y(ω)=G(ω)X(ω),  (4)

where

$\begin{matrix}{{G(\omega)} = {\sum\limits_{n = {- L}}^{L - 1}{{G_{n}\left( {L\; \omega} \right)}{{{P\left( {\omega - {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}} \right)}}^{2}.}}}} & (5)\end{matrix}$

Here,

G_(n)(ω) = Σ_(n)g_(n)(k)exp (− k ω)

is the discrete time Fourier transform of the filter applied in subbandn for n≦0 and

G _(n)(ω)=G _(−1−n)(−ω)* for n<0  . (6)

where * denotes complex conjugation. Observe here that the special caseG_(n)(ω)=1 leads to G(ω)=1 in (5) due to the assumed special design ofthe prototype p(v), which implies

$\begin{matrix}{{\sum\limits_{n = {- L}}^{L - 1}{{P\left( {\omega - {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}} \right)}}^{2}} = 1} & (7)\end{matrix}$

Another case of interest is G_(n)(ω)=exp(−iω) which leads toG(ω)=exp(−iLω), so that y(v)=x(v−L).

Approximating a Given Filter Response by Subband Filtering

Let H(ω) be a given filter (e.g. transfer function) with real valuedimpulse response h(v). This data is considered as input to the filterconverter 104. In view of (5) and (7), a trivial choice for the subbandfilters which result in the desired response G(ω)=H(ω) is given by

G _(n)(ω)=H(ω/L), for |ω−π(n+1/2)|≦π  (8)

The drawback of this formula is that although H(ω) is a smooth functionof ω, the periodized segment of it defined by (8) will exhibit jumps andthe impulse response of the subband filters will be unnecessarily long.The prior art usage of the complex pseudo QMF bank for equalization orenvelope adjustment consists of applying a single gain g_(n) in eachsubband, which results in the transfer function

$\begin{matrix}{{G(\omega)} = {\sum\limits_{n = {- L}}^{L - 1}{g_{n}{{P\left( {\omega - {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}} \right)}}^{2}}}} & (9)\end{matrix}$

with the extension g_(n)=−g_(−1−n)* for n<0 defined in accordance with(6). In view of (7), one achieves

$\begin{matrix}{{{G\left( {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)} \right)} = g_{n}},{{{for}\mspace{14mu} n} = 0},1,\ldots,{L - 1},} & (10)\end{matrix}$

and the transfer function is interpolated between those frequencies. Fortarget filter responses H(ω) that vary slowly as a function of thefrequency ω, a first method of approximating the filter is thereforeobtained by choosing

$\begin{matrix}{{G_{n}(\omega)} = {{H\left( {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)} \right)}.}} & (11)\end{matrix}$

An example of the resulting quality of this procedure is given in FIGS.5 and 7.

According to an embodiment of the present invention a filter generatoror a filter converter 104 is used to teach to convert the filter(defined by its impulse response) h(v) into intermediate subband filters190 by means of the second analysis filter bank 301 which employs realvalued prototype filter q(v),

$\begin{matrix}{{g_{n}(k)} = {\sum\limits_{v = {- \infty}}^{\infty}{{h\left( {v + {kL}} \right)}{q(v)}{{\exp \left( {{- }\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)v} \right)}.}}}} & (12)\end{matrix}$

In terms of Fourier transforms this reads

$\begin{matrix}{{G_{n}(\omega)} = {\frac{1}{L}{\sum\limits_{l = 0}^{L - 1}{{H\left( \frac{\omega + {2\; \pi \; l}}{L} \right)}{{Q\left( {\frac{\omega + {2\; \pi \; l}}{L} - {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}} \right)}^{*}.}}}}} & (13)\end{matrix}$

The advantage of this procedure is that any given filter h(v) can beefficiently transformed into intermediate subband filter responses. Ifq(v) has K_(Q)·L taps, a time domain filter h(v) of K_(H)·L taps isconverted into subband domain filters (12) with K_(H)+K_(Q)−1 taps,wherein K_(H) and H_(Q), are positive integers. With respect to theexemplary numbers given in the context of the description of FIG. 4,K_(H) and K_(Q) are equal to 3 and with a prototype filter length and animpulse response corresponding to a length of 3·64=192 (L=64) each.Hence, each intermediate subband filter 190 has an impulse responselength of only 3+3·1=5 taps each.

Design of the Prototype Filter for the Filter Converter

Insertion of (13) into (5) yields

$\begin{matrix}{{G(\omega)} = {\sum\limits_{l = 0}^{L - 1}{{H\begin{pmatrix}{\omega +} \\{\frac{2\; \pi}{L}l}\end{pmatrix}}{\sum\limits_{n = {- L}}^{L - 1}{\frac{1}{L}{Q\begin{pmatrix}{\omega + {\frac{2\; \pi}{L}l} -} \\{\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}\end{pmatrix}}^{*}{{{P\left( {\omega - {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}} \right)}}^{2}.}}}}}} & (14)\end{matrix}$

Hence, the condition for G(ω)=H(ω) to hold is that

$\begin{matrix}{{{\sum\limits_{n = {- L}}^{L - 1}{\frac{1}{L}{Q\left( {\omega + {\frac{2\; \pi}{L}l} - {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}} \right)}^{*}{{P\left( {\omega - {\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)}} \right)}}^{2}}} = {\delta \lbrack l\rbrack}},} & (15)\end{matrix}$

where δ[l]=1 for l=0 and δ[l]=0 for 1≠0. A simple solution to (15) isgiven by the brick wall filter

${Q(\omega)} = \left\{ \begin{matrix}{L,} & {{{{for}\mspace{14mu} {\omega }} \leq {\pi/L}};} \\{0,} & {{{for}\mspace{14mu} {\pi/L}} < {\omega } \leq {\pi.}}\end{matrix} \right.$

This prototype filter corresponds to the choice (8) and has thedisadvantage of having an infinite and slowly decaying impulse responseq(v). Instead, the present invention teaches to solve (15) approximately(e.g. in the least-square sense) with a finite impulse response filterq(v). The time domain equivalent of (15) is the system of linearequations for n=0, 1 . . . , L−1 and for all integers k,

$\begin{matrix}{{{\sum\limits_{v = {- \infty}}^{\infty}{{p_{2}\left( {n + {vL} - {2\; {kL}}} \right)}{q\left( {n + {vL}} \right)}}} = {\frac{1}{2\; L}{\delta \lbrack k\rbrack}}},} & (16)\end{matrix}$

where

$\begin{matrix}{{p_{2}(v)} = {\sum\limits_{l = {- \infty}}^{\infty}{{p(l)}{p\left( {l + v} \right)}}}} & (17)\end{matrix}$

is the autocorrelation of p(v). For any given support length the systemof linear equations (16) can be solved in the least squares sense for aprototype filter q(v). It is desirable to use a support significantlyshorter than that of the original filter bank prototype filter p(v), andin that case the linear system (16) is over-determined. A given qualityof approximation can also be traded for other desirable properties viajoint optimization. One example of such a property is a low pass type offrequency response Q(ω).

In the following the determination of a multi-slot QMF representation(subband domain) of the HRTF filters is described. The filter conversionfrom the time domain into the complex QMF subband domain is performed byan FIR filter in the filter converter 104 of FIG. 1 a. To be moreprecise, the following description outlines a method for implementing agiven FIR filter h(ν) of length N_(h) in the complex QMF subband domain.The principle of the operation is illustrated in FIG. 1 a in the case ofa system also comprising an embodiment of an inventive filter apparatus.

The subband filtering itself is carried out by a set of or a pluralityof intermediate filters 190 inside the subband filtering 102. To be moreprecise, the subband filtering consist of the separate application ofone complex valued FIR intermediate filter g_(n)(l) for each QMF subbandwith an index n=0, 1, . . . , 63. In other words, in the followingdescription special references will be made to embodiments with L=64different subband signals. Nevertheless, this specific number of subbandsignals is not essential and the appropriate equations will also begiven in a more general form.

One of the key components of the system shown in FIG. 1 a is the filterconverter 104, which converts the given time domain FIR filter h(ν) intothe complex subband domain filters g_(n)(l). The filter converter 104comprises a complex analysis bank 301 similar to the QMF analysis bank101. The prototype filter of the complex analysis filter bank 301 of thefilter converter 104 q(ν) of length 192 (=3.64) for the specific case ofL=64 subband signals are created by solving in the least square sensethe over determined system of the equation (16). The filter coefficientsq(ν) or rather the relations they fulfill will be described in moredetail for the case of L=64 subbands signals later on.

To be more accurate in terms of mathematical description, an extensionwith zeros in the time domain FIR filter is defined by

$\begin{matrix}{{\overset{\sim}{h}(\upsilon)} = \left\{ \begin{matrix}{{h(\upsilon)},} & {{\upsilon = 0},1,\ldots \mspace{14mu},{N_{h} - 1},} \\{0,} & {otherwise}\end{matrix} \right.} & (18)\end{matrix}$

The resulting intermediate subband domain filters are based on equation(12) and can be expressed in the general case as

$\begin{matrix}{{g_{n}(l)} = {\sum\limits_{v = 0}^{N_{q} - 1}{{\overset{\sim}{h}\left( {\upsilon + {L \cdot \left( {l - l_{0}} \right)}} \right)} \cdot {q(\upsilon)} \cdot {\exp \left( {{- }\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)\left( {\upsilon - \upsilon_{0}} \right)} \right)}}}} & (19)\end{matrix}$

wherein l₀ and ν₀ are delays, l is an integer indicating an index of thefilter taps and N_(q) (=N_(Q)) is the length of the impulse response ofthe prototype filter q(ν).

It should be noted, that in the frame work of the present applicationunder an equation being based on an equation an introduction ofadditional delays (cf. l₀ and ν₀) factors, additional coefficients andan introduction of a window function or another simple function isunderstood.

In the case L=64, the expression for the subband domain filters orintermediate filters 190 becomes

$\begin{matrix}{{g_{n}(l)} = {\sum\limits_{v = 0}^{191}{{\overset{\sim}{h}\left( {\upsilon + {64 \cdot \left( {l - 2} \right)}} \right)} \cdot {q(\upsilon)} \cdot {\exp \left( {{- }\frac{\pi}{64}\left( {n + \frac{1}{2}} \right)\left( {\upsilon - 95} \right)} \right)}}}} & (20)\end{matrix}$

These subdomain filters have a length L_(q)=K_(h)+2, where

K _(h) =┌N _(h)/64┐  (21)

and N_(h) is the length of the impulse response h(ν) of the filtercharacteristics to be transferred into the subband domain.

In this case, the integer n=0, 1, . . . , 63 is once again the index ofa subband and l=0, 1, . . . , (K_(h)+1) is an integer indicating taps ofthe resulting intermediate filters 190.

The extra addend of (−2) in equation (20) as compared to equation (12)is there, because equation (12) was developed without any regard tocasualty of filters. Real implementations will cause always introducedelays. Hence, depending on the concrete implementation, additionaldelayers or delays can be implemented in the embodiments shown in FIGS.1 a to 1 e and FIGS. 2 to 11, which have been omitted for the sake ofsimplicity in Figures mentioned.

As outlined earlier, in many cases the system of linear equations (16)is over determined. Nevertheless, it can be solved or approximated inthe least square sense with respect to the prototype filter coefficientsq(ν). Solving the system of linear equations (16) in the least squaresense, leads to the filter taps of the prototype filter q(ν) to fulfillthe following relations for integers ν from 0 to 191:

−0.204≦q[0]≦−0.202

−0.199≦q[1]≦−0.197

−0.194≦q[2]≦−0.192

−0.189≦q[3]≦−0.187

−0.183≦q[4]≦−0.181

−0.178≦q[5]≦−0.176

−0.172≦q[6]≦−0.170

−0.166≦q[7]≦−0.164

−0.160≦q[8]≦−0.158

−0.154≦q[9]≦−0.152

−0.148≦q[10]≦−0.146

−0.142≦q[11]≦−0.140

−0.135≦q[12]≦−0.133

−0.129≦q[13]≦−0.127

−0.122≦q[14]≦−0.120

−0.116≦q[15]≦−0.114

−0.109≦q[16]≦−0.107

−0.102≦q[17]≦−0.100

−0.096≦q[18]≦−0.100

−0.089≦q[19]≦−0.094

−0.082≦q[20]≦−0.087

−0.075≦q[21]≦−0.080

−0.068≦q[22]≦−0.066

−0.061≦q[23]≦−0.059

−0.054≦q[24]≦−0.052

−0.046≦q[25]≦−0.044

−0.039≦q[26]≦−0.037

−0.032≦q[27]≦−0.030

−0.024≦q[28]≦−0.022

−0.017≦q[29]≦−0.015

−0.009≦q[30]≦−0.007

−0.002≦q[31]≦0.000

0.006≦q[32]≦0.008

0.014≦q[33]≦0.016

0.021≦q[34]≦0.023

0.029≦q[35]≦0.031

0.037≦q[36]≦0.039

0.045≦q[37]≦0.047

0.054≦q[38]≦0.056

0.062≦q[39]≦0.064

0.070≦q[40]≦0.072

0.079≦q[41]≦0.081

0.087≦q[42]≦0.089

0.096≦q[43]≦0.098

0.105≦q[44]≦0.107

0.113≦q[45]≦0.115

0.122≦q[46]≦0.124

0.132≦q[47]≦0.134

0.141≦q[48]≦0.143

0.150≦q[49]≦0.152

0.160≦q[50]≦0.162

0.170≦q[51]≦0.172

0.180≦q[52]≦0.182

0.190≦q[53]≦0.192

0.200≦q[54]≦0.202

0.210≦q[55]≦0.212

0.221≦q[56]≦0.223

0.232≦q[57]≦0.234

0.243≦q[58]≦0.245

0.254≦q[59]≦0.256

0.266≦q[60]≦0.268

0.278≦q[61]≦0.280

0.290≦q[62]≦0.292

0.303≦q[63]≦0.305

0.902≦q[64]≦0.904

0.909≦q[65]≦0.911

0.917≦q[66]≦0.919

0.924≦q[67]≦0.926

0.930≦q[68]≦0.932

0.936≦q[69]≦0.938

0.942≦q[70]≦0.944

0.947≦q[71]≦0.949

0.952≦q[72]≦0.954

0.957≦q[73]≦0.959

0.961≦q[74]≦0.963

0.965≦q[75]≦0.967

0.969≦q[76]≦0.971

0.972≦q[77]≦0.974

0.975≦q[78]≦0.977

0.978≦q[79]≦0.980

0.981≦q[80]≦0.983

0.984≦q[81]≦0.986

0.986≦q[82]≦0.988

0.988≦q[83]≦0.990

0.990≦q[84]≦0.992

0.992≦q[85]≦0.994

0.993≦q[86]≦0.995

0.995≦q[87]≦0.997

0.996≦q[88]≦0.998

0.997≦q[891]≦0.999

0.998≦q[90]≦1.000

0.999≦q[91]≦1.001

0.999≦q[92]≦1.001

1.000≦q[93]≦1.002

1.000≦q[94]≦1.002

1.000≦q[95]≦1.002

1.000≦q[96]≦1.002

1.000≦q[97]≦1.002

0.999≦q[98]≦1.001

0.999≦q[99]≦1.001

0.998≦q[100]≦1.000

0.997≦q[101]≦0.999

0.996≦q[102]≦0.998

0.995≦q[103]≦0.997

0.993≦q[104]≦0.995

0.992≦q[105]≦0.994

0.990≦q[106]≦0.992

0.988≦q[107]≦0.990

0.986≦q[108]≦0.988

0.984≦q[109]≦0.986

0.981≦q[110]≦0.983

0.978≦q[111]≦0.980

0.975≦q[112]≦0.977

0.972≦q[113]≦0.974

0.969≦q[114]≦0.971

0.965≦q[115]≦0.967

0.961≦q[116]≦0.963

0.957≦q[117]≦0.959

0.952≦q[118]≦0.954

0.947≦q[119]≦0.949

0.942≦q[120]≦0.944

0.936≦q[121]≦0.938

0.930≦q[122]≦0.932

0.924≦q[123]≦0.926

0.917≦q[124]≦0.919

0.909≦q[125]≦0.911

0.902≦q[126]≦0.904

0.893≦q[127]≦0.895

0.290≦q[128]≦0.292

0.278≦q[129]≦0.280

0.266≦q[130]≦0.268

0.254≦q[131]≦0.256

0.243≦q[132]≦0.245

0.232≦q[133]≦0.234

0.221≦q[134]≦0.223

0.210≦q[135]≦0.212

0.200≦q[136]≦0.202

0.190≦q[137]≦0.192

0.180≦q[138]≦0.182

0.170≦q[139]≦0.172

0.160≦q[140]≦0.162

0.150≦q[141]≦0.152

0.141≦q[142]≦0.143

0.132≦q[143]≦0.134

0.122≦q[144]≦0.124

0.113≦q[145]≦0.115

0.105≦q[146]≦0.107

0.096≦q[147]≦0.098

0.087≦q[148]≦0.089

0.079≦q[149]≦0.081

0.070≦q[150]≦0.072

0.062≦q[151]≦0.064

0.054≦q[152]≦0.056

0.045≦q[153]≦0.047

0.037≦q[154]≦0.039

0.029≦q[155]≦0.031

0.021≦q[156]≦0.023

0.014≦q[157]≦0.016

0.006≦q[158]≦0.008

−0.002≦q[159]≦−0.000

−0.009≦q[160]≦−0.007

−0.017≦q[161]≦−0.015

−0.024≦q[162]≦−0.022

−0.032≦q[163]≦−0.030

−0.039≦q[164]≦−0.037

−0.046≦q[165]≦−0.044

−0.054≦q[166]≦0.052

−0.061≦q[167]≦−0.059

−0.068≦q[168]≦−0.066

−0.075≦q[169]≦−0.073

−0.082≦q[170]≦−0.080

−0.089≦q[171]≦−0.087

−0.096≦q[172]≦−0.094

−0.102≦q[173]≦−0.100

−0.109≦q[174]≦−0.107

−0.116≦q[175]≦−0.114

−0.122≦q[176]≦−0.120

−0.129≦q[177]≦−0.127

−0.135≦q[178]≦−0.133

−0.142≦q[179]≦−0.140

−0.148.5 q[180]≦−0.146

−0.154≦q[181]≦−0.152

−0.160≦q[182]≦−0.158

−0.166≦q[183]≦−0.164

−0.172≦q[184]≦−0.170

−0.178≦q[185]≦−0.176

−0.183≦q[186]≦−0.181

−0.189≦q[187]≦−0.187

−0.194≦q[188]≦−0.192

−0.199≦q[189]≦−0.197

−0.204≦q[190]≦−0.202

−0.209≦q[191]≦−0.207

To be more precise, the filter coefficients q(ν) obey the followingrelations:

−0.20294≦q[0]≦−0.20292

−0.19804≦q[1]≦−0.19.802

−0.19295≦q[2]≦−0.19293

−0.18768≦q[3]≦−0.18766

−0.18226≦q[4]≦−0.18224

−0.17668≦q[5]≦−0.17666

−0.17097≦q[6]≦−0.17095

−0.16514≦q[7]≦−0.16512

−0.15919≦q[8]≦−0.15917

−0.15313≦q[9]≦−0.15311

−0.14697≦q[10]≦−0.14695

−0.14071≦q[11]≦−0.14069

−0.13437≦q[12]≦−0.13435

−0.12794≦q[13]≦−0.12792

−0.12144≦q[14]≦−0.12142

−0.11486≦q[15]≦−0.11484

−0.10821≦q[16]≦−0.10819

−0.10149≦q[17]≦−0.10147

−0.09471≦q[18]≦−0.09469

−0.08786≦q[19]≦−0.08784

−0.08095 q[20]≦−0.08093

−0.07397≦q[21]≦−0.07395

−0.06694≦q[22]≦−0.06692

−0.05984≦q[23]≦0.05982

−0.05269≦q[24]≦−0.05267

−0.04547≦q[25]≦−0.04545

−0.03819≦q[26]≦−0.03817

−0.03085≦q[27]≦−0.03083

−0.02345≦q[28]≦−0.02343

−0.01598≦q[29]≦−0.01596

−0.00845≦q[30]≦−0.00843

−0.00084≦q[31]≦−0.00082

0.00683≦q[32]≦0.00685

0.01458≦q[33]≦0.01460

0.02240≦q[34]≦0.02242

0.03030≦q[35]≦0.03032

0.03828≦q[36]≦0.03830

0.04635≦q[37]≦0.04637

0.05451≦q[38]≦0.05453

0.06275≦q[39]≦0.06277

0.07110≦q[40]≦0.07112

0.07954≦q[41]≦0.07956

0.08809≦q[42]≦0.08811

0.09675≦q[43]≦0.09677

0.10552≦q[44]≦0.10554

0.11442≦q[45]≦0.11444

0.12344≦q[46]≦0.12346

0.13259≦q[47]≦0.13261

0.14189≦q[48]≦0.14191

0.15132≦q[49]≦0.15134

0.16091≦q[50]≦0.16093

0.17066≦q[51]≦0.17068

0.18058≦q[52]≦0.18060

0.19067≦q[53]≦0.19069

0.20095≦q[54]≦0.20097

0.21143≦q[55]≦0.21145

0.22211≦q[56]≦0.22213

0.23300≦q[57]≦0.23302

0.24412≦q[58]≦0.24414

0.25549≦q[59]≦0.25551

0.26711≦q[60]≦0.26713

0.27899≦q[61]≦0.27901

0.29117≦q[62]≦0.29119

0.30364≦q[63]≦0.30366

0.90252≦q[64]≦0.90254

0.91035≦q[65]≦0.91037

0.91769≦q[66]≦0.91771

0.92457≦q[67]≦0.92459

0.93101≦q[68]≦0.93103

0.93705≦q[69]≦0.93707

0.94270≦q[70]≦0.94272

0.94800≦q[71]≦0.94802

0.95295≦q[72]≦0.95297

0.95758≦q[73]≦0.95760

0.96190≦q[74]≦0.96192

0.96593≦q[75]≦0.96595

0.96968≦q[76]≦0.96970

0.97317≦q[77]≦0.97319

0.97641≦q[78]≦0.97643

0.97940≦q[79]≦0.97942

0.98217≦q[80]≦0.98219

0.98472≦q[81]≦0.98474

0.98706≦q[82]≦0.98708

0.98919≦q[83]≦0.98921

0.99113≦q[84]≦0.99115

0.99288≦q[85]≦0.99290

0.99444≦q[86]≦0.99446

0.99583≦q[87]≦0.99585

0.99704≦q[88]≦0.99706

0.99809≦q[89]≦0.99811

0.99896≦q[90]≦0.99898

0.99967≦q[91]≦0.99969

1.00023≦q[92]≦1.00025

1.00062≦q[93]≦1.00064

1.00086≦q[94]≦1.00088

1.00093≦q[95]≦1.00095

1.00086≦q[96]≦1.00088

1.00062≦q[97]≦1.00064

1.00023≦q[98]≦1.00025

0.99967≦q[99]≦0.99969

0.99896≦q[100]≦0.99898

0.99809≦q[101]≦0.99811

0.99704≦q[102]≦0.99706

0.99583≦q[103]≦0.99585

0.99444≦q[104]≦0.99446

0.99288≦q[105]≦0.99290

0.99113≦q[106]≦0.99115

0.98919≦q[107]≦0.98921

0.98706≦q[108]≦0.98708

0.98472≦q[109]≦0.98474

0.98217≦q[110]≦0.98219

0.97940≦q[111]≦0.97942

0.97641≦q[112]≦0.97643

0.97317≦q[113]≦0.97319

0.96968≦q[114]≦0.96970

0.96593≦q[115]≦0.96595

0.96190≦q[116]≦0.96192

0.95758≦q[117]≦0.95760

0.95295≦q[118]≦0.95297

0.94800≦q[119]≦0.94802

0.94270≦q[120]≦0.94272

0.93705≦q[121]≦0.93707

0.93101≦q[122]≦0.93103

0.92457≦q[123]≦0.92459

0.91769≦q[124]≦0.91771

0.91035≦q[125]≦0.91037

0.90252≦q[126]≦0.90254

0.89416≦q[127]≦0.89418

0.29117≦q[128]≦0.29119

0.27899≦q[129]≦0.27901

0.26711≦q[130]≦0.26713

0.25549≦q[131]≦0.25551

0.24412≦q[132]≦0.24414

0.23300≦q[133]≦0.23302

0.22211≦q[134]≦0.22213

0.21143≦q[135]≦0.21145

0.20095≦q[136]≦0.20097

0.19067≦q[137]≦0.19069

0.18058≦q[138]≦0.18060

0.17066≦q[139]≦0.17068

0.16091≦q[140]≦0.16093

0.151325≦q[141]≦0.15134

0.14189≦q[142]≦0.14191

0.13259≦q[143]≦0.13261

0.12344≦q[144]≦0.12346

0.11442≦q[145]≦0.11444

0.10552≦q[146]≦0.10554

0.09675≦q[147]≦0.09677

0.08809≦q[148]≦0.08811

0.07954≦q[149]≦0.07956

0.07110≦q[150]≦0.07112

0.06275≦q[151]≦0.06277

0.05451≦q[152]≦0.05453

0.04635≦q[153]≦0.04637

0.03828≦q[154]≦0.03830

0.03030≦q[155]≦0.03032

0.02240≦q[156]≦0.02242

0.01458≦q[157]≦0.01460

0.00683≦q[158]≦0.00685

−0.00084≦q[159]≦−0.00082

−0.00845≦q[160]≦−0.00843

−0.01598≦q[161]≦−0.01596

−0.02345≦q[162]≦−0.02343

−0.0308523 q[163]≦0.03083

−0.03819≦q[164]≦0.03817

−0.04547≦q[165]≦−0.04545

−0.05269≦q[166]≦0.05267

−0.05984 q[167]≦−0.05982

−0.06694≦q[168]≦0.06692

−0.07397≦q[169]≦−0.07395

−0.08095≦q[170]≦0.08093

−0.08786≦q[171]≦0.08784

−0.09471≦q[172]≦−0.09469

−0.10149≦q[173]≦0.10147

−0.10821≦q[174]≦0.10819

−0.11486≦q[175]≦0.11484

−0.12144≦q[176]≦0.12142

−0.12794≦q[177]≦−0.12792

−0.13437≦q[178]≦−0.13435

−0.14071≦q[179]≦0.14069

−0.14697≦q[180]≦0.14695

−0.15313≦q[181]≦−0.15311

−0.15919≦q[182]≦0.15917

−0.16514≦q[183]≦−0.16512

−0.17097≦q[184]≦−0.17095

−0.17668≦q[185]≦−0.17666

−0.18226≦q[186]≦−0.18224

−0.18768≦q[187]≦−0.18766

−0.19295≦q[188]≦−0.19293

−0.19804≦q[189]≦0.19802

−0.20294≦q[190]≦−0.20292

−0.20764 q[191]≦0.20762

Even more accurately, the filter coefficients q(ν) can be expressed bythe following equations for the integer ν in the range between 0 and191, wherein according to the requirements and specifications of specialimplementations, the prototype filter coefficients may deviate from thefollowing equations either individually or from the maximum absolutevalue typically by 10%, 5% or 2% and preferably by 1% or 0.1%:

q[0]=−0.2029343380

q[1]=−0.1980331588

q[2]=−0.1929411519

q[3]=−0.1876744222

q[4]=−0.1822474011

q[5]=−0.1766730202

q[6]=−0.1709628636

q[7]=−0.1651273005

q[8]=−0.1591756024

q[9]=−0.1531160455

q[10]=−0.1469560005

q[11]=−0.1407020132

q[12]=−0.1343598738

q[13]=−0.1279346790

q[14]=−0.1214308876

q[15]=−0.1148523686

q[16]=−0.1082024454

q[17]=−0.1014839341

q[18]=−0.0946991783

q[19]=−0.0878500799

q[20]=−0.0809381268

q[21]=−0.0739644174

q[22]=−0.0669296831

q[23]=−0.0598343081

q[24]=−0.0526783466

q[25]=−0.0454615388

q[26]=−0.0381833249

q[27]=−0.0308428572

q[28]=−0.0234390115

q[29]=−0.0159703957

q[30]=−0.0084353584

q[31]=−0.0008319956

q[32]=0.0068418435

q[33]=0.0145885527

q[34]=0.0224107648

q[35]=0.0303113495

q[36]=0.0382934126

q[37]=0.0463602959

q[38]=0.0545155789

q[39]=0.0627630810

q[40]=0.0711068657

q[41]=0.0795512453

q[42]=0.0881007879

q[43]=0.0967603259

q[44]=0.1055349658

q[45]=0.1144301000

q[46]=0.1234514222

q[47]=0.1326049434

q[48]=0.1418970123

q[49]=0.1513343370

q[50]=0.1609240126

q[51]=0.1706735517

q[52]=0.1805909194

q[53]=0.1906845753

q[54]=0.2009635191

q[55]=0.2114373458

q[56]=0.2221163080

q[57]=0.2330113868

q[58]=0.2441343742

q[59]=0.2554979664

q[60]=0.2671158700

q[61]=0.2790029236

q[62]=0.2911752349

q[63]=0.3036503350

q[64]=0.9025275713

q[65]=0.9103585196

q[66]=0.9176977825

q[67]=0.9245760683

q[68]=0.9310214581

q[69]=0.9370596739

q[70]=0.9427143143

q[71]=0.9480070606

q[72]=0.9529578566

q[73]=0.9575850672

q[74]=0.9619056158

q[75]=0.9659351065

q[76]=0.9696879297

q[77]=0.9731773547

q[78]=0.9764156119

q[79]=0.9794139640

q[80]=0.9821827692

q[81]=0.9847315377

q[82]=0.9870689790

q[83]=0.9892030462

q[84]=0.9911409728

q[85]=0.9928893067

q[86]=0.9944539395

q[87]=0.9958401318

q[88]=0.9970525352

q[89]=0.9980952118

q[90]=0.9989716504

q[91]=0.9996847806

q[92]=1.0002369837

q[93]=1.0006301028

q[94]=1.0008654482

q[95]=1.0009438063

q[96]=1.0008654482

q[97]=1.0006301028

q[98]=1.0002369837

q[99]=0.9996847806

q[100]=0.9989716504

q[101]=0.9980952118

q[102]=0.9970525352

q[103]=0.9958401318

q[104]=0.9944539395

q[105]=0.9928893067

q[106]=0.9911409728

q[107]=0.9892030462

q[108]=0.9870689790

q[109]=0.9847315377

q[110]=0.9821827692

q[111]=0.9794139640

q[112]=0.9764156119

q[113]=0.9731773547

q[114]=0.9696879297

q[115]=0.9659351065

q[116]=0.9619056158

q[117]=0.9575850672

q[118]=0.9529578566

q[119]=0.9480070606

q[120]=0.9427143143

q[121]=0.9370596739

q[122]=0.9310214581

q[123]=0.9245760683

q[124]=0.9176977825

q[125]=0.9103585196

q[126]=0.9025275713

q[127]=0.8941712974

q[128]=0.2911752349

q[129]=0.2790029236

q[130]=0.2671158700

q[131]=0.2554979664

q[132]=0.2441343742

q[133]=0.2330113868

q[134]=0.2221163080

q[135]=0.2114373458

q[136]=0.2009635191

q[137]=0.1906845753

q[138]=0.1805909194

q[139]=0.1706735517

q[140]=0.1609240126

q[141]=0.1513343370

q[142]=0.1418970123

q[143]=0.1326049434

q[144]=0.1234514222

q[145]=0.1144301000

q[146]=0.1055349658

q[147]=0.0967603259

q[148]=0.0881007879

q[149]=0.0795512453

q[150]=0.0711068657

q[151]=0.0627630810

q[152]=0.0545155789

q[153]=0.0463602959

q[154]=0.0382934126

q[155]=0.0303113495

q[156]=0.0224107648

q[157]=0.0145885527

q[158]=0.0068418435

q[159]=−0.0008319956

q[160]=−0.0084353584

q[161]=−0.0159703957

q[162]=−0.0234390115

q[163]=−0.0308428572

q[164]=−0.0381833249

q[165]=−0.0454615388

q[166]=−0.0526783466

q[167]=−0.0598343081

q[168]=−0.0669296831

q[169]=−0.0739644174

q[170]=−0.0809381268

q[171]=−0.0878500799

q[172]=−0.0946991783

q[173]=−0.1014839341

q[174]=−0.1082024454

q[175]=−0.1148523686

q[176]=−0.1214308876

q[177]=−0.1279346790

q[178]=−0.1343598738

q[179]=−0.1407020132

q[180]=−0.1469560005

q[181]=−0.1531160455

q[182]=−0.1591756024

q[183]=−0.1651273005

q[184]=−0.1709628636

q[185]=−0.1766730202

q[186]=−0.1822474011

q[187]=−0.1876744222

q[188]=−0.1929411519

q[189]=−0.1980331588

q[190]=−0.2029343380

q[191]=−0.2076267137

Hence, the present invention relates to the application of an arbitraryfilter to a signal which is available in the transform domain of acomplex exponential modulated filter bank, when this filter bank isdesigned to give virtually alias free performance of operations likeequalization, spectral envelope adjustment, frequency selective panning,or frequency selective spatialization of audio signals. The presentinvention permits to efficiently transform a given finite impulseresponse (FIR) filter in the time domain into a set of shorter FIRfilters, to be applied with one filter for each subband of the filterbank.

The present invention also teaches how to convert a given discrete timedomain filter into to a set of subband domain filters. The result isthat any given filter can be implemented with a high degree of accuracyin the subband domain of a complex exponential modulated filter bank. Ina preferred embodiment, the filter converter consists of a secondcomplex exponential modulated analysis filter bank. For the special caseof filters that implement a pure delay, the methods of the presentinvention coincides with that of PCT/EP2004/004607 “Advanced processingbased on a complex-exponential modulated filterbank and adaptive timeframing”.

Furthermore, the present invention comprises the following features:

-   -   A method for obtaining a high quality approximation to the        filtering of a discrete-time input signal with a given filter,        comprising the steps of        -   analyzing the input signal with a downsampled complex            analysis filter bank in order to obtain a multitude of            subband signals,        -   filtering each subband signal with a subband filter, where            the multitude of subband filters are obtained from the given            filter by means of a filter converter,        -   synthesizing an output signal from the filtered subband            signals with a downsampled complex synthesis filter bank.    -   A method according to the above where the filter converter        consists of a downsampled complex analysis filter bank.    -   An apparatus for performing a method for obtaining a high        quality approximation to the filtering of a discrete-time input        signal with a given filter, the method comprising the steps of        -   analyzing the input signal with a downsampled complex            analysis filter bank in order to obtain a multitude of            subband signals,        -   filtering each subband signal with a subband filter, where            the multitude of subband filters are obtained from the given            filter by means of a filter converter,        -   synthesizing an output signal from the filtered subband            signals with a downsampled complex synthesis filter bank.    -   A computer program having instructions for performing, when        running on a computer, a method for obtaining a high quality        approximation to the filtering of a discrete-time input signal        with a given filter, the method comprising the steps of        -   analyzing the input signal with a downsampled complex            analysis filter bank in order to obtain a multitude of            subband signals,        -   filtering each subband signal with a subband filter, where            the multitude of subband filters are obtained from the given            filter by means of a filter converter,        -   synthesizing an output signal from the filtered subband            signals with a downsampled complex synthesis filter bank.

Adaptation for Real Cosine Modulated Filter Banks

Whereas the above derivation is based on complex modulated filter banks,a note can be made here for the critically sampled real representationobtained by a cosine modulated filter bank defined by taking the realpart of the subband samples (1) for an appropriate phase factor O. Inthis case it is no longer feasible to use the in-band subband filteringmethod (3) to obtain a good approximation to a given filter. However,due to the assumptions made on the prototype filter response, ageneralization to a multiband filter of the type

$\begin{matrix}{{{d_{n}(k)} = {\sum\limits_{r = {- 1}}^{1}{\sum\limits_{l}{{g_{n}^{r}(l)}{c_{n + r}\left( {k - l} \right)}}}}},} & (22)\end{matrix}$

will be applicable, (with obvious modifications for the first and lastsubbands). Due to the critical sampling there is much less freedom inthe construction of the filter mask g_(n) ^(r)(l). One has to do thefollowing, which is obvious for those skilled in the art. For each m=0,1, . . . , L−1, use the elementary subband signal d_(n)(k)=δ[n−m]δ[k] asinput to the real synthesis bank, and filter the resulting output y(v)with the filter h(v) to get the filtered synthesis waveform z(v). Nowuse this filtered waveform as input to the real analysis bank. Theresulting subband signal carries the coefficients of the masks g_(n)^(r)(l) for n+r=m. Some reduction in work necessary for the filter isobtained by observing that the three cases m=3κ+ε for ε=0,1,2 can beprocessed in parallel by feeding the first synthesis bank with all thecorresponding elementary subband signals for each case. Thus the realvalued filter converter comprises three real synthesis and three realanalysis bank operations. This parallel computation represents animplementation short cut for real valued filter converter for the caseof a QMF band with good side lope suppression.

FIG. 9 illustrates an embodiment of an inventive filter apparatus forfiltering a time domain input signal of an inventive filter apparatus toobtain a time domain output signal. As already mentioned in the contextof FIG. 1 a, the filter apparatus of FIG. 9 comprises a complex analysisfilter bank 101, a subband filtering 102 and a complex synthesis filterbank 103, which outputs the time domain output signal.

While FIG. 1 shows a system comprising an embodiment of an inventivefilter apparatus along with an embodiment of a filter generator 104, thefilter apparatus shown in FIG. 9 comprises only as an option a filterconverter 104, which provides the subband filtering 102 with theintermediate filter definition signal, for instance in the form of thefilter taps or the impulse response for each of the intermediate filters190 of the subband filtering 102. The filter apparatus shown in FIG. 9,comprises additional optional components, which can provide the subbandfiltering 102 with the filter taps for the plurality of intermediatefilters 190 of the subband filtering 102.

As an example, the filter taps can also be taken from an optional database 500, which is connected to the subband filtering 102. In oneembodiment, the data base 500 comprises the complex valued filter tapsof the intermediate filters 190. The data base can be implemented as amemory system, for instance in the form of a non-volatile memory systemor volatile memory system depending on the concrete implementation.Hence, memory solutions for the data base 500 comprise ROM (ROM=readonly memory), RAM (RAM=random access memory), flash memory, magneticalmemory, optical memory or other memory systems.

Depending on the concrete implementation, a processor or a CPU(CPU=central processing unit) 510 can access the data base and providethe filter taps to the subband filtering 102 or can also access the database to provide the corresponding filter taps to the intermediatefilters of the subband filtering 102. Hence, such an embodimentcomprises a data base 500 from which the filter taps for the subbandfiltering 102 can be taken.

In a further embodiment of an inventive filter apparatus, which is alsodepicted as an option in FIG. 9, the CPU 510 is capable of on-linecalculating the filter taps. In such an embodiment, the CPU 510 accessesthe data base 500 according to a set of parameters provided by the userand/or according to a set of parameters, which are based on furthercircumstances, reads one or more sets of filter taps for theintermediate filters of the subband filtering 102 and calculates,optionally accompanied by an interpolation scheme or another estimationscheme, the desired intermediate filter taps and provides them to thesubband filtering 102. In a further embodiment, the CPU 510 or anotherprocessor or computer system provides the filter taps of theintermediate filters 190 to the subband filtering 102 without accessinga data base 500. In such an embodiment, the CPU 510 or another processorcalculates the filter taps and provides them to the subband filtering102. Examples for such an embodiment will be explained more closely withrespect to FIG. 10.

In a further embodiment depicted in FIG. 9, the CPU 510 accesses afurther data base 520, reads one or more filter definition signals (e.g.in the form of impulse response signals corresponding to filtercharacteristic in the time domain), calculates an effective filterdefinition signal, for instance an appropriate impulse response, andprovides the results of this computation to the filter converter 104. Inthis embodiment, the filter converter 104 then provides the subbandfiltering 102 with the appropriate filter taps for the intermediatefilters 190. Hence, in this embodiment, the filter converter 104generates the effective subband filters or intermediate filters appliedto each individual subband filters of each individual subband signalinside the subband filtering 102 leading to a filtering effect audiblyindistinguishable from a corresponding filter applied to the time domaininput signal (input signal). As consequence, this embodiment is alsocapable of on-line calculating the filter taps via the filter converter104.

An example might for instance be a device, which calculates the taps ofthe intermediate filters 190 of the subband filtering 102 according to aset of parameters for instance provided by the user, wherein theparameter basis is so large, that an effective predetermination of thefilter taps, optionally accompanied by some sort of interpolationscheme, would not lead to the desired results.

A more concrete application comes for instance of the field of dynamicchance of HRTF filters in one domain to be converted to the subband orQMF domain. As mentioned before, this is for instance relevant inapplications involving a head-tracker in which the data base 520 is anHRTF data base comprising the time impulse responses of the HRTFfilters. As the HRTF filters usually have very long impulse responses,the use of such a scheme is especially interesting, as the taps for theintermediate filters 190 or the QMF taps are complex. Storing the database in this domain would roughly double the memory requirementscompared to the memory requirement of storing the impulse responses inthe time domain. However, the advantage of the reduced memoryrequirement can also be employed without having a CPU 510 whichcalculates the impulse response provided to the filter converter 504.Instead, the data base 520 can be simply be prompted to output thecorresponding definition signal, which might be an impulse response inthe time domain to the filter converter 104.

In FIG. 10, an amplitude/frequency characteristic 550 is illustrated inthe frequency domain. In some applications, as explained before, thefilter coefficients or filter taps are the intermediate filters 190 ofthe subband filtering 102 can be stored in the data base like the database 500 of FIG. 9. Alternatively or additionally, for someapplications, the filter taps of the intermediate filters can also becalculated by the CPU 510 of FIG. 9. In the case of a special effectfiltering or a lower quality signal processing, in which aliasingeffects might become tolerable (at least to some extend), the filtertaps of the intermediate filters 190 after subband filtering 102 can beestimated without a filter converter 104 or another embodiment of afilter generator. Possible applications especially comprise voicetransmission over low quality lines, like telephones or small band radiocommunications. Hence, in these applications a determination of thefilter taps corresponding the transfer function 550 of FIG. 10 oranother amplitude/frequency characteristic into several subbands 560with different subband frequencies can be carried out without employingan inventive filter converter.

FIG. 11 shows an embodiment of an inventive filter converter 104. Aspreviously outlined in the context of FIG. 3, the filter converter 104comprises a complex analysis filter bank 301 to which a (real valued)impulse response signal indicative of an amplitude/frequency filtercharacteristic can be supplied via an input 104 a and via an optionalswitch 600. As outlined before, the complex analysis filter bank 301converts the impulse response signal into a plurality of complex valuedsubband signals and the intermediate filter definition signal output atan output 104 b of the filter converter. As indicated in FIG. 1 a andFIG. 9, the output 104 b of the filter converter 104 can be connected toa subband filtering 102.

As already mentioned earlier, each of the complex valued subband signalsof the complex modulated filter bank 301 corresponds to an impulseresponse for one of the intermediate filters 190 for a subband signal inthe subband filtering 102 shown in FIGS. 1 a and 9. Typically, thecomplex valued subband signals are significantly shorter than theimpulse response signal of the filter characteristic provided at theinput 104 a in the time domain. Furthermore, typically at least one ofthe complex valued subband signals output at the output 104 b comprisesat least two different non-vanishing values. Especially the last featuredistinguishes the output of the filter converter 104 from a simple gainadjustment in the frame work of filtering using a direct Fouriertransform procedure.

If, however, the filter converter 104 is not provided with an impulseresponse signal indicative of an amplitude/frequency filtercharacteristic, but a filter definition signal, which comprises at leastone of an amplitude/frequency filter characteristic, a phase/frequencyfilter characteristic or the filter taps in the time domain or anotherdomain of a filter, the filter converter 104 comprises an impulseresponse generator 610 for converting the filter definition signal intothe impulse response signal, which is then provided via the optionalswitch 600 to the complex analysis filter bank 301. In a concreteimplementation, the impulse response generator 610 can for instancecalculate the impulse response signal provided to the complex analysisfilter bank 301 by superposition of real valued oscillations (Fouriersynthesis), wherein the amplitude characteristics and the phasecharacteristics of the intended filter to be transferred into thecomplex subband domain are regarded as defined by the definition signalprovided to the input 104 c. In other words, if at least one of anamplitude/frequency characteristic and a phase/frequency characteristicis applied to the impulse response generator 610, an impulse responsesignal can be computed by the impulse response generator 610 bysupposition of (harmonic) oscillations considering the amplitude andphase relations as defined by the filter definition signal.

Possible applications of both embodiments of the filter apparatus andthe filter generator and especially in the field of high quality audiocoding and decoding.

Recent developments in audio coding have provided means to obtain amulti-channel signal impression over stereo headphones. This is commonlydone by downmixing a multi-channel signal to stereo using the originalmulti-channel signal and HRTF filters. It has been shown in prior artthat the parametric multi-channel audio decoder can be combined with abinaural downmix algorithm making it possible to render a multi-channelsignal over headphones without the need for first re-creating themulti-channel signal from the transmitted downmix signal, andsubsequently downmixing it again by means of the HRTF filters. However,this requires that the parameters for recreating the multi-channelsignal (e.g. IID, CLD parameters) are combined with the HRTF filters,which in turn requires a parameterization of the HRTF filters. Thisrequirement for a parameterization of the HRTF filters imposes highlimitation on the system, since HRTF filters can be long and thus veryhard to correctly model with a parametric approach. This limitationmakes it impossible to use long HRTF filters for combined parametricmulti-channel and binaural downmix decoders. The crucial algorithmiccomponent required to obtain a proper combination of multi-channelparameters and HRTF filters is to have access to a representation of thegiven HRTF filters in the subband domain assumed by the spatialparameters. This is exactly what is offered by the embodiments of thepresent invention. Once this representation is available, the HRTFfilters can be combined into 2N filters as a function of the parametricmulti-channel representation. This gives a significant advantage interms of computational complexity over the method that first recreatesthe M channels and then applies 2M filtering operations.

An example of a different application of the method employed byembodiments of the current invention is the efficient compensation fornon-perfect audio rendering devices for audio content coded in the MPEGHE-AAC format [ISO/IEC 14496-3:2001/AMD1:2003]. Such advanced filteringsteps, possibly including cross talk cancellation, can be applieddirectly in the subband domain prior to the time domain synthesis.

Other developments in audio coding has made methods available torecreate a multi-channel representation of an audio signal based on astereo (or mono) signal and corresponding control data. These methodsdiffer substantially from older matrix based solution such as Dolby®Prologic, since additional control data is transmitted to control there-creation, also referred to as up-mix, of the surround channels basedon the transmitted mono or stereo channels.

Hence, such a parametric multi-channel audio decoder, e.g. MPEG Surroundreconstructs N channels based on M transmitted channels, where N>M, andthe additional control data. The additional control data represents asignificantly lower data rate than that required for transmission of allN channels, making the coding very efficient while at the same timeensuring compatibility with both M channel devices and N channeldevices. [J. Breebaart et al. “MPEG spatial audio coding/MPEG Surround:overview and current status”, Proc. 119th AES convention, New York, USA,October 2005, Preprint 6447].

These parametric surround coding methods usually comprise aparameterization of the surround signal based on Channel LevelDifference (CLD) and Inter-channel coherence/cross-correlation (ICC).These parameters describe power ratios and correlation between channelpairs in the up-mix process. Further Channel Prediction Coefficients(CPC) are also used in prior art to predict intermediate or outputchannels during the up-mix procedure.

Depending on certain implementation requirements of the inventivemethods, the inventive methods can be implemented in hardware or insoftware. The implementation can be performed using a digital storagemedium, in particular a disc, CD or a DVD having an electronicallyreadable control signal stop thereon, which cooperates with aprogrammable computer system in such that an embodiment of the inventivemethods is performed. Generally, an embodiment of the present inventionis, therefore, a computer program product with a program code stored onan machine-readable carrier, the program code being operative forperforming the inventive methods when the computer program product runson a computer or a processor. In other words, embodiments of theinventive methods are, therefore, a computer program having a programcode for performing at least one of the inventive methods when thecomputer program runs of a computer.

While the foregoing has been particularly shown and described withreferences to particular embodiments thereof, it will be understood bythose skilled in the art that various other changes in the form anddetails maybe made without departing from the spiritual scope thereof.It is to be understood that various changes may be made in adapting todifferent embodiments without departing from the broader conceptdisclosed herein and comprehend by the claims that follows.

1. Filter apparatus for filtering a time domain input signal to obtain atime domain output signal, which is a representation of the time domaininput signal filtered using a filter characteristic having annon-uniform amplitude/frequency characteristic, comprising: a complexanalysis filter bank for generating a plurality of complex subbandsignals from the time domain input signals; a plurality of intermediatefilters, wherein at least one of the intermediate filters of theplurality of the intermediate filters has a non-uniformamplitude/frequency characteristic, wherein the plurality ofintermediate filters have a shorter impulse response compared to animpulse response of a filter having the filter characteristic, andwherein the non-uniform amplitude/frequency characteristics of theplurality of intermediate filters together represent the non-uniformfilter characteristic; and a complex synthesis filter bank forsynthesizing the output of the intermediate filters to obtain the timedomain output signal.
 2. Filter apparatus according to claim 1, whereinat least one of the immediate filters has a low pass filtercharacteristic, a high pass filter characteristic, a band pass filtercharacteristic, a band rejection filter characteristic or a notch filtercharacteristic.
 3. Filter apparatus according to claim 1, wherein theintermediate filters of the plurality of intermediate filters are finiteimpulse response filters.
 4. Filter apparatus according to claim 1,wherein each intermediate filter is operative to have an impulseresponse depending on an intermediate filter definition signal. 5.Filter apparatus according to claim 4, wherein the plurality ofintermediate filter is operative to receive the intermediate filterdefinition signal from a data base or from a processor.
 6. Filterapparatus according to claim 4, wherein the plurality of intermediatefilters is operative to receive the intermediate filter definitionsignal from a filter generator comprising a complex modulated filterbank for filtering an impulse response signal indicative of anamplitude/frequency filter characteristic in a time domain to obtain aplurality of complex valued subband signals as the intermediate filterdefinition signal, wherein each complex valued subband signal of thecomplex modulated filter bank corresponds to an impulse response for oneintermediate filter, wherein at least one of the complex valued subbandsignals comprises at least two different non-vanishing values, andwherein each complex valued subband signal is shorter than the impulseresponse signal.
 7. Filter apparatus according to claim 1, wherein thecomplex analysis filter bank is operative to output L complex subbandsignals, wherein the plurality of intermediate filters comprises Lintermediate filters, wherein the complex synthesis filter bank isoperative to synthesize the output of the L intermediate filters, andwherein L is a positive integer greater than
 1. 8. Filter apparatusaccording to claim 7, wherein the complex analysis filter bank, theplurality of intermediate filters and the complex synthesis filter bankis operative to have L=64.
 9. Filter apparatus according to claim 7,wherein the plurality of intermediate filters is operative to filter thecomplex subband signals based on the equation $\begin{matrix}{{d_{n}(k)} = {\sum\limits_{l}{{g_{n}(l)}{c_{n}\left( {k - l} \right)}}}} & (3)\end{matrix}$ wherein n is an integer in the range from 0 to (L−1)indicating an index of the subband signals, wherein L and k areintegers, wherein d_(n)(k) is the output of the intermediate filter(190) of the subband signal with the index n, wherein c_(n)(k) is thesubband signal with the index n, and wherein g_(n)(l) is the impulseresponse of the intermediate filter for the subband signal with theindex n.
 10. Filter apparatus according to claim 7, wherein theintermediate filter with an index n has an impulse response g_(n)(k),which is based on the equation $\begin{matrix}{{g_{n}(k)} = {\sum\limits_{v = {- \infty}}^{\infty}{{h\left( {v + {kL}} \right)}{q(v)}{\exp \left( {{- }\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)v} \right)}}}} & (12)\end{matrix}$ wherein n is an integer in the range from 0 to (L−1)indicating the index of the subband signal, wherein k and v areintegers, wherein h(ν) is the response of a filter having the filtercharacteristic, wherein n=3.1415926 . . . is the circular number,wherein i=√{square root over (−1)} is the complex unit, and wherein q(ν)are filter taps of a real valued prototype filter.
 11. Filter apparatusaccording to claim 7, wherein at least one of the intermediate filterswith an index n has an impulse response g_(n)(k), which is based on theequation $\begin{matrix}{{g_{n}(l)} = {\sum\limits_{v = 0}^{191}{{\overset{\sim}{h}\left( {\upsilon + {64 \cdot \left( {l - 2} \right)}} \right)} \cdot {q(\upsilon)} \cdot {\exp \left( {{- }\frac{\pi}{64}\left( {n + \frac{1}{2}} \right)\left( {\upsilon - 95} \right)} \right)}}}} & (20)\end{matrix}$ wherein $\begin{matrix}{{\overset{\sim}{h}(\upsilon)} = \left\{ \begin{matrix}{{h(\upsilon)},} & {{\upsilon = 0},1,\ldots \mspace{14mu},{N_{h} - 1},} \\{0,} & {otherwise}\end{matrix} \right.} & (18)\end{matrix}$ wherein N_(h), is the length of the impulse response h(o)of a filter having the filter characteristic, wherein π=3.1415926 . . .is the circular number, wherein i=√{square root over (−1)} is thecomplex unit, and wherein q(o) are filter taps of a real valuedprototype filter.
 12. Filter apparatus according to claim 10, whereinthe intermediate filters are adapted so that the prototype filter tapsq(ν) fulfil for integers ν from 0 to 191 the relations:−0.204≦q[0]≦−0.202−0.199≦q[1]≦−0.197−0.194≦q[2]≦−0.192−0.189≦q[3]≦−0.187−0.183≦q[4]≦−0.181−0.178≦q[5]≦−0.176−0.172≦q[6]≦−0.170−0.166≦q[7]≦−0.164−0.160≦q[8]≦−0.158−0.154≦q[9]≦−0.152−0.148≦q[10]≦−0.146−0.142≦q[11]≦−0.140−0.135≦q[12]≦−0.133−0.129≦q[13]≦−0.127−0.122≦q[14]≦−0.120−0.116≦q[15]≦−0.114−0.109≦q[16]≦−0.107−0.102≦q[17]≦−0.100−0.096≦q[18]≦−0.100−0.089≦q[19]≦−0.094−0.082≦q[20]≦−0.087−0.075≦q[21]≦−0.080−0.068≦q[22]≦−0.066−0.061≦q[23]≦−0.059−0.054≦q[24]≦−0.052−0.046≦q[25]≦−0.044−0.039≦q[26]≦−0.037−0.032≦q[27]≦−0.030−0.024≦q[28]≦−0.022−0.017≦q[29]≦−0.015−0.009≦q[30]≦−0.007−0.002≦q[31]≦0.0000.006≦q[32]≦0.0080.014≦q[33]≦0.0160.021≦q[34]≦0.0230.029≦q[35]≦0.0310.037≦q[36]≦0.0390.045≦q[37]≦0.0470.054≦q[38]≦0.0560.062≦q[39]≦0.0640.070≦q[40]≦0.0720.079≦q[41]≦0.0810.087≦q[42]≦0.0890.096≦q[43]≦0.0980.105≦q[44]≦0.1070.113≦q[45]≦0.1150.122≦q[46]≦0.1240.132≦q[47]≦0.1340.141≦q[48]≦0.1430.150≦q[49]≦0.1520.160≦q[50]≦0.1620.170≦q[51]≦0.1720.180≦q[52]≦0.1820.190≦q[53]≦0.1920.200≦q[54]≦0.2020.210≦q[55]≦0.2120.221≦q[56]≦0.2230.232≦q[57]≦0.2340.243≦q[58]≦0.2450.254≦q[59]≦0.2560.266≦q[60]≦0.2680.278≦q[61]≦0.2800.290≦q[62]≦0.2920.303≦q[63]≦0.3050.902≦q[64]≦0.9040.909≦q[65]≦0.9110.917≦q[66]≦0.9190.924≦q[67]≦0.9260.930≦q[68]≦0.9320.936≦q[69]≦0.9380.942≦q[70]≦0.9440.947≦q[71]≦0.9490.952≦q[72]≦0.9540.957≦q[73]≦0.9590.961≦q[74]≦0.9630.965≦q[75]≦0.9670.969≦q[76]≦0.9710.972≦q[77]≦0.9740.975≦q[78]≦0.9770.978≦q[79]≦0.9800.981≦q[80]≦0.9830.984≦q[81]≦0.9860.986≦q[82]≦0.9880.988≦q[83]≦0.9900.990≦q[84]≦0.9920.992≦q[85]≦0.9940.993≦q[86]≦0.9950.995≦q[87]≦0.9970.996≦q[88]≦0.9980.997≦q[891]≦0.9990.998≦q[90]≦1.0000.999≦q[91]≦1.0010.999≦q[92]≦1.0011.000≦q[93]≦1.0021.000≦q[94]≦1.0021.000≦q[95]≦1.0021.000≦q[96]≦1.0021.000≦q[97]≦1.0020.999≦q[98]≦1.0010.999≦q[99]≦1.0010.998≦q[100]≦1.0000.997≦q[101]≦0.9990.996≦q[102]≦0.9980.995≦q[103]≦0.9970.993≦q[104]≦0.9950.992≦q[105]≦0.9940.990≦q[106]≦0.9920.988≦q[107]≦0.9900.986≦q[108]≦0.9880.984≦q[109]≦0.9860.981≦q[110]≦0.9830.978≦q[111]≦0.9800.975≦q[112]≦0.9770.972≦q[113]≦0.9740.969≦q[114]≦0.9710.965≦q[115]≦0.9670.961≦q[116]≦0.9630.957≦q[117]≦0.9590.952≦q[118]≦0.9540.947≦q[119]≦0.9490.942≦q[120]≦0.9440.936≦q[121]≦0.9380.930≦q[122]≦0.9320.924≦q[123]≦0.9260.917≦q[124]≦0.9190.909≦q[125]≦0.9110.902≦q[126]≦0.9040.893≦q[127]≦0.8950.290≦q[128]≦0.2920.278≦q[129]≦0.2800.266≦q[130]≦0.2680.254≦q[131]≦0.2560.243≦q[132]≦0.2450.232≦q[133]≦0.2340.221≦q[134]≦0.2230.210≦q[135]≦0.2120.200≦q[136]≦0.2020.190≦q[137]≦0.1920.180≦q[138]≦0.1820.170≦q[139]≦0.1720.160≦q[140]≦0.1620.150≦q[141]≦0.1520.141≦q[142]≦0.1430.132≦q[143]≦0.1340.122≦q[144]≦0.1240.113≦q[145]≦0.1150.105≦q[146]≦0.1070.096≦q[147]≦0.0980.087≦q[148]≦0.0890.079≦q[149]≦0.0810.070≦q[150]≦0.0720.062≦q[151]≦0.0640.054≦q[152]≦0.0560.045≦q[153]≦0.0470.037≦q[154]≦0.0390.029≦q[155]≦0.0310.021≦q[156]≦0.0230.014≦q[157]≦0.0160.006≦q[158]≦0.008−0.002≦q[159]≦−0.000−0.009≦q[160]≦−0.007−0.017≦q[161]≦−0.015−0.024≦q[162]≦−0.022−0.032≦q[163]≦−0.030−0.039≦q[164]≦−0.037−0.046≦q[165]≦−0.044−0.054≦q[166]≦0.052−0.061≦q[167]≦−0.059−0.068≦q[168]≦−0.066−0.075≦q[169]≦−0.073−0.082≦q[170]≦−0.080−0.089≦q[171]≦−0.087−0.096≦q[172]≦−0.094−0.102≦q[173]≦−0.100−0.109≦q[174]≦−0.107−0.116≦q[175]≦−0.114−0.122≦q[176]≦−0.120−0.129≦q[177]≦−0.127−0.135≦q[178]≦−0.133−0.142≦q[179]≦−0.140−0.148.5 q[180]≦−0.146−0.154≦q[181]≦−0.152−0.160≦q[182]≦−0.158−0.166≦q[183]≦−0.164−0.172≦q[184]≦−0.170−0.178≦q[185]≦−0.176−0.183≦q[186]≦−0.181−0.189≦q[187]≦−0.187−0.194≦q[188]≦−0.192−0.199≦q[189]≦−0.197−0.204≦q[190]≦−0.202−0.209≦q[191]≦−0.207
 13. Filter apparatus according to claim 10, whereinthe intermediate filters are adapted so that the prototype filter tapsq(ν) fulfil for integers ν from 0 to 191 the relations:−0.20294≦q[0]≦−0.20292−0.19804≦q[1]≦−0.19.802−0.19295≦q[2]≦−0.19293−0.18768≦q[3]≦−0.18766−0.18226≦q[4]≦−0.18224−0.17668≦q[5]≦−0.17666−0.17097≦q[6]≦−0.17095−0.16514≦q[7]≦−0.16512−0.15919≦q[8]≦−0.15917−0.15313≦q[9]≦−0.15311−0.14697≦q[10]≦−0.14695−0.14071≦q[11]≦−0.14069−0.13437≦q[12]≦−0.13435−0.12794≦q[13]≦−0.12792−0.12144≦q[14]≦−0.12142−0.11486≦q[15]≦−0.11484−0.10821≦q[16]≦−0.10819−0.10149≦q[17]≦−0.10147−0.09471≦q[18]≦−0.09469−0.08786≦q[19]≦−0.08784−0.08095 q[20]≦−0.08093−0.07397≦q[21]≦−0.07395−0.06694≦q[22]≦−0.06692−0.05984≦q[23]≦0.05982−0.05269≦q[24]≦−0.05267−0.04547≦q[25]≦−0.04545−0.03819≦q[26]≦−0.03817−0.03085≦q[27]≦−0.03083−0.02345≦q[28]≦−0.02343−0.01598≦q[29]≦−0.01596−0.00845≦q[30]≦−0.0.0843−0.00084≦q[31]≦−0.000820.00683≦q[32]≦0.006850.01458≦q[33]≦0.014600.02240≦q[34]≦0.022420.03030≦q[35]≦0.030320.03828≦q[36]≦0.038300.04635≦q[37]≦0.046370.05451≦q[38]≦0.054530.06275≦q[39]≦0.062770.07110≦q[40]≦0.071120.07954≦q[41]≦0.079560.08809≦q[42]≦0.088110.09675≦q[43]≦0.096770.10552≦q[44]≦0.105540.11442≦q[45]≦0.114440.12344≦q[46]≦0.123460.13259≦q[47]≦0.132610.14189≦q[48]≦0.141910.15132≦q[49]≦0.151340.16091≦q[50]≦0.160930.17066≦q[51]≦0.170680.18058≦q[52]≦0.180600.19067≦q[53]≦0.190690.20095≦q[54]≦0.200970.21143≦q[55]≦0.211450.22211≦q[56]≦0.222130.23300≦q[57]≦0.233020.24412≦q[58]≦0.244140.25549≦q[59]≦0.255510.26711≦q[60]≦0.267130.27899≦q[61]≦0.279010.29117≦q[62]≦0.291190.30364≦q[63]≦0.303660.90252≦q[64]≦0.902540.91035≦q[65]≦0.910370.91769≦q[66]≦0.917710.92457≦q[67]≦0.924590.93101≦q[68]≦0.931030.93705≦q[69]≦0.937070.94270≦q[70]≦0.942720.94800≦q[71]≦0.948020.95295≦q[72]≦0.952970.95758≦q[73]≦0.957600.96190≦q[74]≦0.961920.96593≦q[75]≦0.965950.96968≦q[76]≦0.969700.97317≦q[77]≦0.973190.97641≦q[78]≦0.976430.97940≦q[79]≦0.979420.98217≦q[80]≦0.982190.98472≦q[81]≦0.984740.98706≦q[82]≦0.987080.98919≦q[83]≦0.989210.99113≦q[84]≦0.991150.99288≦q[85]≦0.992900.99444≦q[86]≦0.994460.99583≦q[87]≦0.995850.99704≦q[88]≦0.997060.99809≦q[89]≦0.998110.99896≦q[90]≦0.998980.99967≦q[91]≦0.999691.00023≦q[92]≦1.000251.00062≦q[93]≦1.000641.00086≦q[94]≦1.000881.00093≦q[95]≦1.000951.00086≦q[96]≦1.000881.00062≦q[97]≦1.000641.00023≦q[98]≦1.000250.99967≦q[99]≦0.999690.99896≦q[100]≦0.998980.99809≦q[101]≦0.998110.99704≦q[102]≦0.997060.99583≦q[103]≦0.995850.99444≦q[104]≦0.994460.99288≦q[105]≦0.992900.99113≦q[106]≦0.991150.98919≦q[107]≦0.989210.98706≦q[108]≦0.987080.98472≦q[109]≦0.984740.98217≦q[110]≦0.982190.97940≦q[111]≦0.979420.97641≦q[112]≦0.976430.97317≦q[113]≦0.973190.96968≦q[114]≦0.969700.96593≦q[115]≦0.965950.96190≦q[116]≦0.961920.95758≦q[117]≦0.957600.95295≦q[118]≦0.952970.94800≦q[119]≦0.948020.94270≦q[120]≦0.942720.93705≦q[121]≦0.937070.93101≦q[122]≦0.931030.92457≦q[123]≦0.924590.91769≦q[124]≦0.917710.91035≦q[125]≦0.910370.90252≦q[126]≦0.902540.89416≦q[127]≦0.894180.29117≦q[128]≦0.291190.27899≦q[129]≦0.279010.26711≦q[130]≦0.267130.25549≦q[131]≦0.255510.24412≦q[132]≦0.244140.23300≦q[133]≦0.233020.22211≦q[134]≦0.222130.21143≦q[135]≦0.211450.20095≦q[136]≦0.200970.19067≦q[137]≦0.190690.18058≦q[138]≦0.180600.17066≦q[139]≦0.170680.16091≦q[140]≦0.160930.151325≦q[141]≦0.151340.14189≦q[142]≦0.141910.13259≦q[143]≦0.132610.12344≦q[144]≦0.123460.11442≦q[145]≦0.114440.10552≦q[146]≦0.105540.09675≦q[147]≦0.096770.08809≦q[148]≦0.088110.07954≦q[149]≦0.079560.07110≦q[150]≦0.071120.06275≦q[151]≦0.062770.05451≦q[152]≦0.054530.04635≦q[153]≦0.046370.03828≦q[154]≦0.038300.03030≦q[155]≦0.030320.02240≦q[156]≦0.022420.01458≦q[157]≦0.014600.00683≦q[158]≦0.00685−0.00084≦q[159]≦−0.00082−0.00845≦q[160]≦−0.00843−0.01598≦q[161]≦−0.01596−0.02345≦q[162]≦−0.02343−0.03085≦q[163]≦−0.03083−0.03819≦q[164]≦−0.03817−0.04547≦q[165]≦−0.04545−0.05269≦q[166]≦−0.05267−0.05984≦q[167]≦−0.05982−0.06694≦q[168]≦−0.06692−0.07397≦q[169]≦−0.07395−0.08095≦q[170]≦−0.08093−0.08786≦q[171]≦−0.08784−0.09471≦q[172]≦−0.09469−0.10149≦q[173]≦−0.10147−0.10821≦q[174]≦−0.10819−0.11486≦q[175]≦−0.11484−0.12144≦q[176]≦−0.12142−0.12794≦q[177]≦−0.12792−0.13437≦q[178]≦−0.13435−0.14071≦q[179]≦−0.14069−0.14697≦q[180]≦−0.14695−0.15313≦q[181]≦−0.15311−0.15919≦q[182]≦−0.15917−0.16514≦q[183]≦−0.16512−0.17097≦q[184]≦−0.17095−0.17668≦q[185]≦−0.17666−0.18226≦q[186]≦−0.18224−0.18768≦q[187]≦−0.18766−0.19295≦q[188]≦−0.19293−0.19804≦q[189]≦−0.19802−0.20294≦q[190]≦−0.20292−0.20764≦q[191]≦−0.20762
 14. Filter apparatus according to claim 10,wherein the intermediate filters are adapted, so that the real valuedprototype filter coefficients q(ν) for integer ν in the range from 0 to191 are given byq[0]=−0.2029343380q[1]=−0.1980331588q[2]=−0.1929411519q[3]=−0.1876744222q[4]=−0.1822474011q[5]=−0.1766730202q[6]=−0.1709628636q[7]=−0.1651273005q[8]=−0.1591756024q[9]=−0.1531160455q[10]=−0.1469560005q[11]=−0.1407020132q[12]=−0.1343598738q[13]=−0.1279346790q[14]=−0.1214308876q[15]=−0.1148523686q[16]=−0.1082024454q[17]=−0.1014839341q[18]=−0.0946991783q[19]=−0.0878500799q[20]=−0.0809381268q[21]=−0.0739644174q[22]=−0.0669296831q[23]=−0.0598343081q[24]=−0.0526783466q[25]=−0.0454615388q[26]=−0.0381833249q[27]=−0.0308428572q[28]=−0.0234390115q[29]=−0.0159703957q[30]=−0.0084353584q[31]=−0.0008319956q[32]=0.0068418435q[33]=0.0145885527q[34]=0.0224107648q[35]=0.0303113495q[36]=0.0382934126q[37]=0.0463602959q[38]=0.0545155789q[39]=0.0627630810q[40]=0.0711068657q[41]=0.0795512453q[42]=0.0881007879q[43]=0.0967603259q[44]=0.1055349658q[45]=0.1144301000q[46]=0.1234514222q[47]=0.1326049434q[48]=0.1418970123q[49]=0.1513343370q[50]=0.1609240126q[51]=0.1706735517q[52]=0.1805909194q[53]=0.1906845753q[54]=0.2009635191q[55]=0.2114373458q[56]=0.2221163080q[57]=0.2330113868q[58]=0.2441343742q[59]=0.2554979664q[60]=0.2671158700q[61]=0.2790029236q[62]=0.2911752349q[63]=0.3036503350q[64]=0.9025275713q[65]=0.9103585196q[66]=0.9176977825q[67]=0.9245760683q[68]=0.9310214581q[69]=0.9370596739q[70]=0.9427143143q[71]=0.9480070606q[72]=0.9529578566q[73]=0.9575850672q[74]=0.9619056158q[75]=0.9659351065q[76]=0.9696879297q[77]=0.9731773547q[78]=0.9764156119q[79]=0.9794139640q[80]=0.9821827692q[81]=0.9847315377q[82]=0.9870689790q[83]=0.9892030462q[84]=0.9911409728q[85]=0.9928893067q[86]=0.9944539395q[87]=0.9958401318q[88]=0.9970525352q[89]=0.9980952118q[90]=0.9989716504q[91]=0.9996847806q[92]=1.0002369837q[93]=1.0006301028q[94]=1.0008654482q[95]=1.0009438063q[96]=1.0008654482q[97]=1.0006301028q[98]=1.0002369837q[99]=0.9996847806q[100]=0.9989716504q[101]=0.9980952118q[102]=0.9970525352q[103]=0.9958401318q[104]=0.9944539395q[105]=0.9928893067q[106]=0.9911409728q[107]=0.9892030462q[108]=0.9870689790q[109]=0.9847315377q[110]=0.9821827692q[111]=0.9794139640q[112]=0.9764156119q[113]=0.9731773547q[114]=0.9696879297q[115]=0.9659351065q[116]=0.9619056158q[117]=0.9575850672q[118]=0.9529578566q[119]=0.9480070606q[120]=0.9427143143q[121]=0.9370596739q[122]=0.9310214581q[123]=0.9245760683q[124]=0.9176977825q[125]=0.9103585196q[126]=0.9025275713q[127]=0.8941712974q[128]=0.2911752349q[129]=0.2790029236q[130]=0.2671158700q[131]=0.2554979664q[132]=0.2441343742q[133]=0.2330113868q[134]=0.2221163080q[135]=0.2114373458q[136]=0.2009635191q[137]=0.1906845753q[138]=0.1805909194q[139]=0.1706735517q[140]=0.1609240126q[141]=0.1513343370q[142]=0.1418970123q[143]=0.1326049434q[144]=0.1234514222q[145]=0.1144301000q[146]=0.1055349658q[147]=0.0967603259q[148]=0.0881007879q[149]=0.0795512453q[150]=0.0711068657q[151]=0.0627630810q[152]=0.0545155789q[153]=0.0463602959q[154]=0.0382934126q[155]=0.0303113495q[156]=0.0224107648q[157]=0.0145885527q[158]=0.0068418435q[159]=−0.0008319956q[160]=−0.0084353584q[161]=−0.0159703957q[162]=−0.0234390115q[163]=−0.0308428572q[164]=−0.0381833249q[165]=−0.0454615388q[166]=−0.0526783466q[167]=−0.0598343081q[168]=−0.0669296831q[169]=−0.0739644174q[170]=−0.0809381268q[171]=−0.0878500799q[172]=−0.0946991783q[173]=−0.1014839341q[174]=−0.1082024454q[175]=−0.1148523686q[176]=−0.1214308876q[177]=−0.1279346790q[178]=−0.1343598738q[179]=−0.1407020132q[180]=−0.1469560005q[181]=−0.1531160455q[182]=−0.1591756024q[183]=−0.1651273005q[184]=−0.1709628636q[185]=−0.1766730202q[186]=−0.1822474011q[187]=−0.1876744222q[188]=−0.1929411519q[189]=−0.1980331588q[190]=−0.2029343380q[191]=−0.2076267137
 15. Filter apparatus according to claim 1, whereinthe filter characteristic is based on an HRTF filter characteristic. 16.Filter apparatus according to claim 1, wherein the complex analysisfilter bank comprises a downsampler for each subband signal output bythe complex analysis filter bank.
 17. Filter apparatus according toclaim 16, wherein the complex analysis filter bank is adapted to outputL complex subband signals, wherein L is a positive integer greater than1, and wherein each of the downsampler is adapted to downsample thesubband signals by a factor of L.
 18. Filter apparatus according toclaim 1, wherein the complex analysis filter bank comprises a complexmodulated filter for each complex subband signal based on a prototypefilter.
 19. Filter apparatus according to claim 1, wherein the complexsynthesis filter bank comprises an upsampler for each of the subbandsignals.
 20. Filter apparatus according to claim 19, wherein the complexsynthesis filter bank is operative to synthesize L signals of theintermediate filters to obtain the time domain output signal, wherein Lis a positive integer greater than 1, wherein the complex synthesisfilter bank comprises L upsampler and wherein each of the upsampler isadapted for upsampling the output of the intermediate filters by afactor of L.
 21. Filter apparatus according to claim 1, wherein thecomplex synthesis filter bank comprises for each subband signal anintermediate synthesis filter, wherein the complex synthesis filter bankcomprises a real part extractor for each signal output by intermediatesynthesis filters, and wherein the complex synthesis filter bank furthercomprises an adder for adding the output of each of a the real partextractor to obtain the time domain output signal.
 22. Filter apparatusaccording to claim 1, wherein the complex synthesis filter bankcomprises an intermediate synthesis filter for each of the subbandsignals output by the intermediate filters, wherein the complexsynthesis filter bank further comprises an adder for summing up theouputs of each intermediate synthesis filters and wherein the complexsynthesis filter bank further comprises a real part extractor forextracting a real valued signal as the time domain output signal fromthe output of the adder.
 23. Filter apparatus according to claim 1,wherein the filter apparatus further comprises a gain adjuster for atleast one subband signal or for at least one signal output byintermediate filter for adjusting the gain.
 24. Filtering apparatusaccording to claim 1, wherein the filtering apparatus further comprisesa further intermediate filter for filtering at least one of the complexvalued subband signals or for filtering at least one of the signalsoutput by one of the intermediate filters.
 25. Filter generator forproviding an intermediate filter definition signal, comprising: acomplex modulated filter bank for filtering an impulse response signalindicative of an amplitude/frequency filter characteristic in a timedomain to obtain a plurality of complex valued subband signals as theintermediate filter definition signal, wherein each complex valuedsubband signal of the complex modulated filter bank corresponds to animpulse response for an intermediate filter for a subband signal;wherein at least one of the complex valued subband signals comprises atleast two different non-vanishing values; and wherein each complexvalued subband signal is shorter than the impulse response signal. 26.Filter generator according to claim 25, wherein the complex modulatedfilter bank is adapted for outputting at least one complex valuedsubband signal as a linear combination of at least two values of theimpulse response signal.
 27. Filter generator according to claim 25,wherein the complex modulated filter bank is adapted for filtering animpulse response signal of a non-uniform amplitude/frequency filtercharacteristic.
 28. Filter generator according to claim 25, wherein thecomplex modulated filter bank is operative to filter the impulseresponse signal, and wherein the impulse response signal is based on aHRTF-related impulse response.
 29. Filter generator according to claim25, wherein the complex modulated filter bank is adapted to output Lcomplex valued subband signals, wherein L is a positive integer greaterthan
 1. 30. Filter generator according to claim 29, wherein the complexmodulated filter bank is adapted for providing the L complex valuedsubband signals downsampled by a factor L.
 31. Filter generatoraccording to claim 29, wherein the complex modulated filter bank isadapted to output L=64 complex valued subband signals.
 32. Filtergenerator according to claim 29, wherein the complex modulated filterbank is adapted to provide complex valued subband signals having valuesg_(n)(k) based on the equation $\begin{matrix}{{g_{n}(k)} = {\sum\limits_{v = {- \infty}}^{\infty}{{h\left( {v + {kL}} \right)}{q(v)}{\exp \left( {{- }\frac{\pi}{L}\left( {n + \frac{1}{2}} \right)v} \right)}}}} & (12)\end{matrix}$ wherein n is an integer in the range from 0 to (L−1)indicating an index of the complex valued subband signal, wherein k andν are integers, wherein h(ν) is the response of a filter having thefilter characteristic, wherein π=3.1415926 . . . is the circular number,wherein i=√{square root over (−1)} is the complex unit, and wherein q(ν)are filter taps of a real valued prototype filter.
 33. Filter generatoraccording to claim 29, wherein the complex modulated filter bank isadapted to provide complex valued subband signals having a value ofg_(n)(k) based on the equation $\begin{matrix}{{g_{n}(l)} = {\sum\limits_{v = 0}^{191}{{\overset{\sim}{h}\left( {\upsilon + {64 \cdot \left( {l - 2} \right)}} \right)} \cdot {q(\upsilon)} \cdot {\exp \left( {{- }\frac{\pi}{64}\left( {n + \frac{1}{2}} \right)\left( {\upsilon - 95} \right)} \right)}}}} & (20)\end{matrix}$ wherein $\begin{matrix}{{\overset{\sim}{h}(\upsilon)} = \left\{ \begin{matrix}{{h(\upsilon)},} & {{\upsilon = 0},1,\ldots \mspace{14mu},{N_{h} - 1},} \\{0,} & {otherwise}\end{matrix} \right.} & (18)\end{matrix}$ wherein N_(h), is the length of the impulse response h(ν)of a filter having the filter characteristic, wherein π=3.1415926 . . .is the circular number, wherein i=√{square root over (−1)} is thecomplex unit, and wherein q(ν) are filter taps of a real valuedprototype filter.
 34. Filter generator according to claim 32, whereinthe complex modulated filter bank is adapted so that the prototypefilter taps q(ν) fulfil for integers ν from 0 to 191 the relations:−0.204≦q[0]≦−0.202−0.199≦q[1]≦−0.197−0.194≦q[2]≦−0.192−0.189 q[3]≦−0.187−0.183≦q[4]≦−0.181−0.178≦q[5]≦−0.176−0.172≦q[6]≦−0.170−0.166≦q[7]≦−0.164−0.160≦q[8]≦−0.158−0.154≦q[9]≦0.152−0.148≦q[10]≦−0.146−0.142≦q[11]≦−0.140−0.135≦q[12]≦−0.133−0.129≦q[13]≦−0.127−0.122 q[14]≦−0.120−0.116≦q[15]≦−0.114−0.109≦q[16]≦−0.107−0.102≦q[17]≦−0.100−0.096≦q[18]≦−0.094−0.089≦q[19]≦−0.087−0.082≦q[20]≦−0.080−0.075≦q[21]≦−0.073−0.068≦q[22]≦−0.066−0.061≦q[23]≦−0.059−0.054≦q[24]≦−0.052−0.046≦q[25]≦−0.044−0.039≦q[26]≦−0.037−0.032≦q[27]≦−0.030−0.024≦q[28]≦−0.022−0.017≦q[29]≦−0.015−0.009≦q[30]≦−−0.007−0.002≦q[31]≦0.0000.006≦q[32]≦0.0080.014≦q[33]≦0.0160.021≦q[34]≦0.0230.029≦q[35]≦0.0310.037≦q[36]≦0.0390.045≦q[37]≦0.0470.054≦q[38]≦0.0560.062≦q[39]≦0.0640.070≦q[40]≦0.0720.079≦q[41]≦0.0810.087≦q[42]≦0.0890.096≦q[43]≦0.0980.105≦q[44]≦0.1070.113≦q[45]≦0.1150.122≦q[46]≦0.1240.132≦q[47]≦0.1340.141≦q[48]≦0.1430.150≦q[49]≦0.1520.160≦q[50]≦0.1620.170≦q[51]≦0.1720.180≦q[52]≦0.1820.190≦q[53]≦0.1920.200≦q[54]≦0.2020.210≦q[55]≦0.2120.221≦q[56]≦0.2230.232≦q[57]≦0.2340.243≦q[58]≦0.2450.254≦q[59]≦0.2560.266≦q[60]≦0.2680.278≦q[61]≦0.2800.290≦q[62]≦0.2920.303≦q[63]≦0.3050.902≦q[64]≦0.9040.909≦q[65]≦0.9110.917≦q[66]≦0.9190.924≦q[67]≦0.9260.930≦q[68]≦0.9320.936≦q[69]≦0.9380.942≦q[70]≦0.9440.947≦q[71]≦0.9490.952≦q[72]≦0.9540.957≦q[73]≦0.9590.961≦q[74]≦0.9630.965≦q[75]≦0.9670.969≦q[76]≦0.9710.972≦q[77]≦0.9740.975≦q[78]≦0.9770.978≦q[79]≦0.9800.981≦q[80]≦0.9830.984≦q[81]≦0.9860.986≦q[82]≦0.9880.988≦q[83]≦0.9900.990≦q[84]≦0.9920.992≦q[85]≦0.9940.993≦q[86]≦0.9950.995≦q[87]≦0.9970.996≦q[88]≦0.9980.997≦q[891]≦0.9990.998≦q[90]≦1.0000.999≦q[91]≦1.0010.999≦q[92]≦1.0011.000≦q[93]≦1.0021.000≦q[94]≦1.0021.000≦q[95]≦1.0021.000≦q[96]≦1.0021.000≦q[97]≦1.0020.999≦q[98]≦1.0010.999≦q[99]≦1.0010.998≦q[100]≦1.0000.997≦q[101]≦0.9990.996≦q[102]≦0.9980.995≦q[103]≦0.9970.993≦q[104]≦0.9950.992≦q[105]≦0.9940.990≦q[106]≦0.9920.988≦q[107]≦0.9900.986≦q[108]≦0.9880.984≦q[109]≦0.9860.981≦q[110]≦0.9830.978≦q[111]≦0.9800.975≦q[112]≦0.9770.972≦q[113]≦0.9740.969≦q[114]≦0.9710.965≦q[115]≦0.9670.961≦q[116]≦0.9630.957≦q[117]≦0.9590.952≦q[118]≦0.9540.947≦q[119]≦0.9490.942≦q[120]≦0.9440.936≦q[121]≦0.9380.930≦q[122]≦0.9320.924≦q[123]≦0.9260.917≦q[124]≦0.9190.909≦q[125]≦0.9110.902≦q[126]≦0.9040.893≦q[127]≦0.8950.290≦q[128]≦0.2920.278≦q[129]≦0.2800.266≦q[130]≦0.2680.254≦q[131]≦0.2560.243≦q[132]≦0.2450.232≦q[133]≦0.2340.221≦q[134]≦0.2230.210≦q[135]≦0.2120.200≦q[136]≦0.2020.190≦q[137]≦0.1920.180≦q[138]≦0.1820.170≦q[139]≦0.1720.160≦q[140]≦0.1620.150≦q[141]≦0.1520.141≦q[142]≦0.1430.132≦q[143]≦0.1340.122≦q[144]≦0.1240.113≦q[145]≦0.1150.105≦q[146]≦0.1070.096≦q[147]≦0.0980.087≦q[148]≦0.0890.079≦q[149]≦0.0810.070≦q[150]≦0.0720.062≦q[151]≦0.0640.054≦q[152]≦0.0560.045≦q[153]≦0.0470.037≦q[154]≦0.0390.029≦q[155]≦0.0310.021≦q[156]≦0.0230.014≦q[157]≦0.0160.006≦q[158]≦0.008−0.002≦q[159]≦0.000−0.009≦q[160]≦−0.007−0.017≦q[161]≦−0.015−0.024≦q[162]≦−0.022−0.032≦q[163]≦−0.030−0.039≦q[164]≦−0.037−0.046≦q[165]≦−0.044−0.054≦q[166]≦−0.052−0.061≦q[167]≦−0.059−0.068≦q[168]≦0.066−0.075≦q[169]≦−0.073−0.082≦q[170]≦−0.080−0.089≦q[171]≦−0.087−0.096≦q[172]≦−0.094−0.102≦q[173]≦−0.100−0.109≦q[174]≦−0.107−0.116≦q[175]≦−0.114−0.122≦q[176]≦−0.120−0.129≦q[177]≦−0.127−0.135≦q[178]≦−0.133−0.142≦q[179]≦−0.140−0.148≦q[180]≦−0.146−0.154≦q[181]≦−0.152−0.160≦q[182]≦−0.158−0.166≦q[183]≦−0.164−0.172≦q[184]≦−0.170−0.178≦q[185]≦−0.176−0.183≦q[186]≦−0.181−0.189≦q[187]≦−0.187−0.194≦q[188]≦−0.192−0.199≦q[189]≦−0.197−0.204≦q[190]≦−0.202−0.209≦q[191]≦−0.207.
 35. Filter generator according to claim 32,wherein the complex modulated filter bank is adapted so that theprototype filter q(ν) fulfils for integers ν from 0 to 191 therelations:−0.20294≦q[0]≦−0.20292−0.19804≦q[1]≦−0.19802−0.19295≦q[2]≦−0.19293−0.18768≦q[3]≦−0.18766−0.18226≦q[4]≦−0.18224−0.17668≦q[5]≦−0.17666−0.17097≦q[6]≦−0.17095−0.16514≦q[7]≦−0.16512−0.15919≦q[8]≦−0.15917−0.15313≦q[9]≦−0.15311−0.14697≦q[10]≦−0.14695−0.14071≦q[11]≦−0.14069−0.13437≦q[12]≦−0.13435−0.12794≦q[13]≦−0.12792−0.12144≦q[14]≦−0.12142−0.11486≦q[15]≦−0.11484−0.10821≦q[16]≦−0.10819−0.10149≦q[17]≦−0.10147−0.09471≦q[18]≦−0.09469−0.08786≦q[19]≦−0.08784−0.08095≦q[20]≦−0.08093−0.07397≦q[21]≦−0.07395−0.06694≦q[22]≦−0.06692−0.05984≦q[23]≦−0.05982−0.05269≦q[24]≦0.05267−0.04547≦q[25]≦−0.04545−0.03819≦q[26]≦−0.03817−0.03085≦q[27]≦−0.03083−0.02345≦q[28]≦−0.02343−0.01598≦q[29]≦−0.01596−0.00845≦q[30]≦−0.00843−0.00084≦q[31]≦0.000820.00683≦q[32]≦0.006850.01458≦q[33]≦0.014600.02240≦q[34]≦0.022420.03030≦q[35]≦0.030320.03828≦q[36]≦0.038300.04635≦q[37]≦0.046370.05451≦q[38]≦0.054530.06275≦q[39]≦0.062770.07110≦q[40]≦0.071120.07954≦q[41]≦0.079560.08809≦q[42]≦0.088110.09675≦q[43]≦0.096770.10552≦q[44]≦0.105540.11442≦q[45]≦0.114440.12344≦q[46]≦0.123460.13259≦q[47]≦0.132610.14189≦q[48]≦0.141910.15132≦q[49]≦0.151340.16091≦q[50]≦0.160930.17066≦q[51]≦0.170680.18058≦q[52]≦0.180600.19067≦q[53]≦0.190690.20095≦q[54]≦0.200970.21143≦q[55]≦0.211450.22211≦q[56]≦0.222130.23300≦q[57]≦0.233020.24412≦q[58]≦0.244140.25549≦q[59]≦0.255510.26711≦q[60]≦0.267130.27899≦q[61]≦0.279010.29117≦q[62]≦0.291190.30364≦q[63]≦0.303660.90252≦q[64]≦0.902540.91035≦q[65]≦0.910370.91769≦q[66]≦0.917710.92457≦q[67]≦0.924590.93101≦q[68]≦0.931030.93705≦q[69]≦0.937070.94270≦q[70]≦0.942720.94800≦q[71]≦0.948020.95295≦q[72]≦0.952970.95758≦q[73]≦0.957600.96190≦q[74]≦0.961920.96593≦q[75]≦0.965950.96968≦q[76]≦0.969700.97317≦q[77]≦0.973190.97641≦q[78]≦0.976430.97940≦q[79]≦0.979420.98217≦q[80]≦0.982190.98472≦q[81]≦0.984740.98706≦q[82]≦0.987080.98919≦q[83]≦0.989210.99113≦q[84]≦0.991150.99288≦q[85]≦0.992900.99444≦q[86]≦0.994460.99583≦q[87]≦0.995850.99704≦q[88]≦0.997060.99809≦q[89]≦0.998110.99896≦q[90]≦0.998980.99967≦q[91]≦0.999691.00023≦q[92]≦1.000251.00062≦q[93]≦1.000641.00086≦q[94]≦1.000881.00093≦q[95]≦1.000951.00086≦q[96]≦1.000881.00062≦q[97]≦1.000641.00023≦q[98]≦1.000250.99967≦q[99]≦0.999690.99896≦q[100]≦0.998980.99809≦q[101]≦0.998110.99704≦q[102]≦0.997060.99583≦q[103]≦0.995850.99444≦q[104]≦0.994460.99288≦q[105]≦0.992900.99113≦q[106]≦0.991150.98919≦q[107]≦0.989210.98706≦q[108]≦0.987080.98472≦q[109]≦0.984740.98217≦q[110]≦0.982190.97940≦q[111]≦0.979420.97641≦q[112]≦0.976430.97317≦q[113]≦0.973190.96968≦q[114]≦0.969700.96593≦q[115]≦0.965950.96190≦q[116]≦0.961920.95758≦q[117]≦0.957600.95295≦q[118]≦0.952970.94800≦q[119]≦0.948020.94270≦q[120]≦0.942720.93705≦q[121]≦0.937070.93101≦q[122]≦0.931030.92457≦q[123]≦0.924590.91769≦q[124]≦0.917710.91035≦q[125]≦0.910370.90252≦q[126]≦0.902540.89416≦q[127]≦0.894180.29117≦q[128]≦0.291190.27899≦q[129]≦0.279010.26711≦q[130]≦0.267130.25549≦q[131]≦0.255510.24412≦q[132]≦0.244140.23300≦q[133]≦0.233020.22211≦q[134]≦0.222130.21143≦q[135]≦0.211450.20095≦q[136]≦0.200970.19067≦q[137]≦0.190690.18058≦q[138]≦0.180600.17066≦q[139]≦0.170680.16091≦q[140]≦0.160930.15132≦q[141]≦0.151340.14189≦q[142]≦0.141910.13259≦q[143]≦0.132610.12344≦q[144]≦0.123460.11442≦q[145]≦0.114440.10552≦q[146]≦0.105540.09675≦q[147]≦0.096770.08809≦q[148]≦0.088110.07954≦q[149]≦0.079560.07110≦q[150]≦0.071120.06275≦q[151]≦0.062770.05451≦q[152]≦0.054530.04635≦q[153]≦0.046370.03828≦q[154]≦0.038300.03030≦q[155]≦0.030320.02240≦q[156]≦0.022420.01458≦q[157]≦0.014600.00683≦q[158]≦0.006850.00084≦q[159]≦−0.00082−0.00845≦q[160]≦−0.00843−0.01598 q[161]≦0.01596−0.02345≦q[162]≦0.02343−0.03085≦q[163]≦−0.03083−0.03819≦q[164]≦−0.03817−0.04547≦q[165]≦−0.04545−0.05269≦q[166]≦0.05267−0.05984≦q[167]≦0.05982−0.06694≦q[168]≦0.06692−0.07397≦q[169]≦−0.07395−0.08095≦q[170]≦−0.08093−0.08786≦q[171]≦−0.08784−0.09471≦q[172]≦−0.09469−0.10149≦q[173]≦−0.10147−0.10821≦q[174]≦−0.10819−0.11486≦q[175]≦−0.11484−0.12144≦q[176]≦−0.12142−0.12794≦q[177]≦−0.12792−0.13437≦q[178]≦−0.13435−0.14071≦q[179]≦−0.14069−0.14697≦q[180]≦−0.14695−0.15313≦q[181]≦−0.15311−0.15919≦q[182]≦−0.15917−0.16514≦q[183]≦−0.16512−0.17097≦q[184]≦−0.17095−0.17668≦q[185]≦−0.17666−0.18226≦q[186]≦−0.18224−0.18768≦q[187]≦−0.18766−0.19295≦q[188]≦−0.19293−0.19804≦q[189]≦−0.19802−0.20294≦q[190]≦−0.20292−0.20764≦q[191]≦−0.20762
 36. Filter generator according to claim 32,wherein the complex modulated filter bank is adapted so that the realvalued prototype filter coefficients q(ν) for integer ν in the rangefrom 0 to 191 are given byq[0]=−0.2029343380q[1]=−0.1980331588q[2]=−0.1929411519q[3]=−0.1876744222q[4]=−0.1822474011q[5]=−0.1766730202q[6]=−0.1709628636q[7]=−0.1651273005q[8]=−0.1591756024q[9]=−0.1531160455q[10]=−0.1469560005q[11]=−0.1407020132q[12]=−0.1343598738q[13]=−0.1279346790q[14]=−0.1214308876q[15]=−0.1148523686q[16]=−0.1082024454q[17]=−0.1014839341q[18]=−0.0946991783q[19]=−0.0878500799q[20]=−0.0809381268q[21]≦0.0739.644174q[22]=−0.0669296831q[23]=−0.0598343081q[24]=−0.0526783466q[25]=−0.0454615388q[26]=−0.0381833249q[27]=−0.0308428572q[28]=−0.0234390115q[29]=−0.0159703957q[30]=−0.0084353584q[31]=−0.0008319956q[32]=0.0068418435q[33]=0.0145885527q[34]=0.0224107648q[35]=0.0303113495q[36]=0.0382934126q[37]=0.0463602959q[38]=0.0545155789q[39]=0.0627630810q[40]=0.0711068657q[41]=0.0795512453q[42]=0.0881007879q[43]=0.0967603259q[44]=0.1055349658q[45]=0.1144301000q[46]=0.1234514222q[47]=0.1326049434q[48]=0.1418970123q[49]=0.1513343370q[50]=0.1609240126q[51]=0.1706735517q[52]=0.1805909194q[53]=0.1906845753q[54]=0.2009635191q[55]=0.2114373458q[56]=0.2221163080q[57]=0.2330113868q[58]=0.2441343742q[59]=0.2554979664q[60]=0.2671158700q[61]=0.2790029236q[62]=0.2911752349q[63]=0.3036503350q[64]=0.9025275713q[65]=0.9103585196q[66]=0.9176977825q[67]=0.9245760683q[68]=0.9310214581q[69]=0.9370596739q[70]=0.9427143143q[71]=0.9480070606q[72]=0.9529578566q[73]=0.9575850672q[74]=0.9619056158q[75]=0.9659351065q[76]=0.9696879297q[77]=0.9731773547q[78]=0.9764156119q[79]=0.9794139640q[80]=0.9821827692q[81]=0.9847315377q[82]=0.9870689790q[83]=0.9892030462q[84]=0.9911409728q[85]=0.9928893067q[86]=0.9944539395q[87]=0.9958401318q[88]=0.9970525352q[89]=0.9980952118q[90]=0.9989716504q[91]=0.9996847806q[92]=1.0002369837q[93]=1.0006301028q[94]=1.0008654482q[95]=1.0009438063q[96]=1.0008654482q[97]=1.0006301028q[98]=1.0002369837q[99]=0.9996847806q[100]=0.9989716504q[101]=0.9980952118q[102]=0.9970525352q[103]=0.9958401318q[104]=0.9944539395q[105]=0.9928893067q[106]=0.9911409728q[107]=0.9892030462q[108]=0.9870689790q[109]=0.9847315377q[110]=0.9821827692q[111]=0.9794139640q[112]=0.9764156119q[113]=0.9731773547q[114]=0.9696879297q[115]=0.9659351065q[116]=0.9619056158q[117]=0.9575850672q[118]=0.9529578566q[119]=0.9480070606q[120]=0.9427143143q[121]=0.9370596739q[122]=0.9310214581q[123]=0.9245760683q[124]=0.9176977825q[125]=0.9103585196q[126]=0.9025275713q[127]=0.8941712974q[128]=0.2911752349q[129]=0.2790029236q[130]=0.2671158700q[131]=0.2554979664q[132]=0.2441343742q[133]=0.2330113868q[134]=0.2221163080q[135]=0.2114373458q[136]=0.2009635191q[137]=0.1906845753q[138]=0.1805909194q[139]=0.1706735517q[140]=0.1609240126q[141]=0.1513343370q[142]=0.1418970123q[143]=0.1326049434q[144]=0.1234514222q[145]=0.1144301000q[146]=0.1055349658q[147]=0.0967603259q[148]=0.0881007879q[149]=0.0795512453q[150]=0.0711068657q[151]=0.0627630810q[152]=0.0545155789q[153]=0.0463602959q[154]=0.0382934126q[155]=0.0303113495q[156]=0.0224107648q[157]=0.0145885527q[158]=0.0068418435q[159]=−0.0008319956q[160]≦0.0084353584q[161]≦0.0159703957q[162]=−0.0234390115q[163]=−0.0308428572q[164]=−0.0381833249q[165]=−0.0454615388q[166]=−0.0526783466q[167]=−0.0598343081q[168]=−0.0669296831q[169]=−0.0739644174q[170]=−0.0809381268q[171]=−0.0878500799q[172]=−0.0946991783q[173]=−0.1014839341q[174]=−0.1082024454q[175]=−0.1148523686q[176]=−0.1214308876q[177]=−0.1279346790q[178]=−0.1343598738q[179]=−0.1407020132q[180]=−0.1469560005q[181]=−0.1531160455q[182]=−0.1591756024q[183]=−0.1651273005q[184]=−0.1709628636q[185]=−0.1766730202q[186]=−0.1822474011q[187]=−0.1876744222q[188]=−0.1929411519q[189]=−0.1980331588q[190]=−0.2029343380q[191]=−0.2076267137
 37. Filter generator according to claim 25, whereinthe complex modulated filter bank further comprises a gain adjuster foradjusting at least one complex valued subband signal with respect to itsvalue before outputting the gain adjusted complex valued subband signalas the intermediate filter definition signal.
 38. Filter, generatoraccording to claim 25, wherein the complex modulated filter bank furthercomprises an impulse response generator for generating the impulseresponse signal based on a filter definition signal provided to thefilter generator, wherein the impulse response signal output by theimpulse response generator is provided to the complex modulated filterbank.
 39. Filter generator according to claim 38, wherein the impulseresponse generator is adapted for generating the impulse response signalbased on at least one of an amplitude/frequency filter characteristic, aphase/frequency filter characteristic and a signal comprising a set offilter taps indicative of the amplitude/frequency filter characteristicin the time domain as a filter definition signal.
 40. Filter system forfiltering the time domain input signal to obtain time domain outputsignal, comprising: a filter apparatus for filtering the time domaininput signal to obtain the time domain output signal, which is arepresentation of the time domain input signal filtered using a filtercharacteristic having an non-uniform amplitude/frequency characteristic,comprising: a complex analysis filter bank for generating a plurality ofcomplex subband signals from the time domain input signals; a pluralityof intermediate filters, wherein at least one of the intermediatefilters of the plurality of the intermediate filters has a non-uniformamplitude/frequency characteristic, wherein the plurality ofintermediate filters have a shorter impulse response compared to animpulse response of a filter having the filter characteristic, andwherein the non-uniform amplitude/frequency characteristics of theplurality of intermediate filters together represent the non-uniformfilter characteristic; and a complex synthesis filter bank forsynthesizing the output of the intermediate filters to obtain the timedomain output signal; and a filter generator for providing anintermediate filter definition signal, comprising: a complex modulatedfilter bank for filtering an impulse response signal indicative of anamplitude/frequency filter characteristic in a time domain to obtain aplurality of complex valued subband signals as the intermediate filterdefinition signal, wherein each complex valued subband signal of thecomplex modulated filter bank corresponds to an impulse response for anintermediate filter for a subband signal; wherein at least one of thecomplex valued subband signals comprises at least two differentnon-vanishing values; and wherein each complex valued subband signal isshorter than the impulse response signal, wherein the filter generatoris coupled to the filter apparatus to provide the plurality of theintermediate filters with an intermediate filter definition; and whereinthe plurality of intermediate filters of the filter apparatus areadapted to have impulse responses based on the intermediate filterdefinition signal.
 41. Method for filtering the time domain input signalto obtain a time domain output signal, which is a representation of thetime domain input signal filtered using a filter characteristic having anon-uniform amplitude/frequency characteristic, comprising the steps:generating a plurality of complex subband signals based on a complexfiltering of the time domain input signal; filtering each of the complexsubband signals, wherein at least one of the complex subband signals isfiltered using an non-uniform amplitude/frequency characteristic,wherein each of the subband signals is filtered based on an impulseresponse being shorter than the impulse response of a filter having thefilter characteristic, and wherein the non-uniform amplitude/frequencycharacteristic of the impulse responses used for filtering the pluralityof subband signals together represent the non-uniform filtercharacteristic; and synthesizing from the output of the filtering of thecomplex subband signals the time domain output signal.
 42. Method forproviding an intermediate filter definition signal, comprising thesteps: filtering an impulse response signal indicative of anamplitude/frequency filter characteristic in a time domain to obtain aplurality of complex valued subband signals as the intermediate filterdefinition signal, wherein each complex valued subband signalcorresponds to an impulse response for an intermediate filter forsubband signal; wherein at least one of the complex valued subbandsignals comprises at least two different non-vanishing values; andwherein each complex valued subband signal is shorter than the impulseresponse signal.
 43. Computer program for performing, when running on acomputer, a method for filtering the time domain input signal to obtaina time domain output signal, which is a representation of the timedomain input signal filtered using a filter characteristic having anon-uniform amplitude/frequency characteristic, comprising the steps:generating a plurality of complex subband signals based on a complexfiltering of the time domain input signal; filtering each of the complexsubband signals, wherein at least one of the complex subband signals isfiltered using an non-uniform amplitude/frequency characteristic,wherein each of the subband signals is filtered based on an impulseresponse being shorter than the impulse response of a filter having thefilter characteristic, and wherein the non-uniform amplitude/frequencycharacteristic of the impulse responses used for filtering the pluralityof subband signals together represent the non-uniform filtercharacteristic; and synthesizing from the output of the filtering of thecomplex subband signals the time domain output signal.
 44. Computerprogram for performing, when running on a computer, a method forproviding an intermediate filter definition signal, comprising thesteps: filtering an impulse response signal indicative of anamplitude/frequency filter characteristic in a time domain to obtain aplurality of complex valued subband signals as the intermediate filterdefinition signal, wherein each complex valued subband signalcorresponds to an impulse response for an intermediate filter forsubband signal; wherein at least one of the complex valued subbandsignals comprises at least two different non-vanishing values; andwherein each complex valued subband signal is shorter than the impulseresponse signal.